Question

# The ratio of base to the height of a triangle is 16: 10 and its area is 80 m². Find the height and base of such a triangle.

Hint:

### Use formula Area of the triangle

## The correct answer is: h = 10 = 10 m

### Let Base, b = 16x and Height, h = 10x

Area of the triangle = 80 m^{2}

= 80

80x^{2} = 80

x^{2} = 1 ⇒ x = 1 , -1

Since sides are always positive so x = 1

Base, b = 16x= 16 m

Height, h = 10 = 10 m

### Related Questions to study

### If the perimeter of an equilateral triangle is 420 units. find half of its area.

It is given that Perimeter of the triangle = 342 units

3 a = 420

a = 140 units

Area of equilateral triangle = a

^{2}

= (140)

^{2}= 4900 sq. units

= 8487.04 sq. units

half of its area=1 = 4243.52

### If the perimeter of an equilateral triangle is 420 units. find half of its area.

It is given that Perimeter of the triangle = 342 units

3 a = 420

a = 140 units

Area of equilateral triangle = a

^{2}

= (140)

^{2}= 4900 sq. units

= 8487.04 sq. units

half of its area=1 = 4243.52

### The base of a triangle is four times its height. What is the area of the triangle?

It is given that base = 4 height

⇒ b = 4h

Area of the triangle =

=

= 2h

^{2}

### The base of a triangle is four times its height. What is the area of the triangle?

It is given that base = 4 height

⇒ b = 4h

Area of the triangle =

=

= 2h

^{2}

### If the perimeter of an equilateral triangle is 342 units. Then find its area.

It is given that Perimeter of the triangle = 342 units

3 a = 342

a = 114 units

Area of equilateral triangle = a

^{2}

= 114

^{2}= 3249 sq. units

= 5627.43 sq. units

### If the perimeter of an equilateral triangle is 342 units. Then find its area.

It is given that Perimeter of the triangle = 342 units

3 a = 342

a = 114 units

Area of equilateral triangle = a

^{2}

= 114

^{2}= 3249 sq. units

= 5627.43 sq. units

### A star is made up of 4 equilateral triangles and a square. If the sides of the triangles are 8 units, what is the surface area of the star ?

Area of equilateral triangle = a

^{2}

= 8

^{2}= 16 square units

Since there are 4 triangles, so area of four equilateral triangles

= 4 16 = 64 sq. units

= 110.85 sq. units

In the figure, length of the side of square = 8 units

Now, Area of square = (side)

^{2}= 8

^{2}= 64 sq. units

Surface Area of the star

= Area of 4 equilateral triangles + Area of the square

= 110.85 + 64 = 174.85 sq. units

### A star is made up of 4 equilateral triangles and a square. If the sides of the triangles are 8 units, what is the surface area of the star ?

Area of equilateral triangle = a

^{2}

= 8

^{2}= 16 square units

Since there are 4 triangles, so area of four equilateral triangles

= 4 16 = 64 sq. units

= 110.85 sq. units

In the figure, length of the side of square = 8 units

Now, Area of square = (side)

^{2}= 8

^{2}= 64 sq. units

Surface Area of the star

= Area of 4 equilateral triangles + Area of the square

= 110.85 + 64 = 174.85 sq. units

### If the side AC of a given triangle is 18 units and the height of the triangle is 10 units, what is the area of triangle ABC ?

Area of the triangle =

= = 90 sq. units

### If the side AC of a given triangle is 18 units and the height of the triangle is 10 units, what is the area of triangle ABC ?

Area of the triangle =

= = 90 sq. units

### A triangle has an area of 90 𝑚^{2} and a base of 12 m, find the height of such a triangle?

area of the triangle = 90 m

^{2}

= 90

= 90

### A triangle has an area of 90 𝑚^{2} and a base of 12 m, find the height of such a triangle?

area of the triangle = 90 m

^{2}

= 90

= 90

### If the height to base ratio of a triangle ABC is 3:4 and the area is 864 square units. Determine the height and base of this triangle.

⇒ Height, h = 3x and Base, b = 4x

Area of triangle =

864 =

864 = 6x

^{2}

144 = x

^{2}

12 = x

Height = 3x = 3(12) = 36 units and Base = 4x = 4(12) = 48 units

### If the height to base ratio of a triangle ABC is 3:4 and the area is 864 square units. Determine the height and base of this triangle.

⇒ Height, h = 3x and Base, b = 4x

Area of triangle =

864 =

864 = 6x

^{2}

144 = x

^{2}

12 = x

Height = 3x = 3(12) = 36 units and Base = 4x = 4(12) = 48 units

### If the side of an equilateral triangular park is 20 units. What will be half of its area ?

^{2}

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^{2}

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^{2}

= 20

^{2}= 100 cm

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### If the base of a triangle becomes three times its height. What is the new area of a triangle?

It is given that base = 3 height

⇒ b = 3h

Area of the triangle =

=

=h

^{2}

### If the base of a triangle becomes three times its height. What is the new area of a triangle?

It is given that base = 3 height

⇒ b = 3h

Area of the triangle =

=

=h

^{2}

### The side of an equilateral triangle is 16 units. What will be the double of its area ?

Area of an equilateral triangle = a

^{2}= 16

^{2}

= 64 cm

^{2}

Double of the area = 2 64

= 128 = 221.7 cm

^{2}

### The side of an equilateral triangle is 16 units. What will be the double of its area ?

Area of an equilateral triangle = a

^{2}= 16

^{2}

= 64 cm

^{2}

Double of the area = 2 64

= 128 = 221.7 cm

^{2}

### In triangle ABC, AB = 8cm. If the altitudes corresponding to AB and BC are 4 cm and 5 cm respectively. Find the measure of BC.

Area of the triangle with altitude corresponding to AB

=

= = 16 cm

^{2}

With Base = BC , Height, h = AE = 5 cm

Area of the triangle with altitude corresponding to BC is

= 16 cm

^{2}

= 16

BC = 6.4 cm

### In triangle ABC, AB = 8cm. If the altitudes corresponding to AB and BC are 4 cm and 5 cm respectively. Find the measure of BC.

Area of the triangle with altitude corresponding to AB

=

= = 16 cm

^{2}

With Base = BC , Height, h = AE = 5 cm

Area of the triangle with altitude corresponding to BC is

= 16 cm

^{2}

= 16

BC = 6.4 cm

### The base and corresponding altitude of a parallelogram are 18 cm and 6 cm respectively. Find its area

Area of the parallelogram = b h

= 18 6 = 108 cm

^{2}

### The base and corresponding altitude of a parallelogram are 18 cm and 6 cm respectively. Find its area

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= 18 6 = 108 cm

^{2}

### The ratio of the bases of two triangles is a : b. If the ratio of their corresponding altitudes is c : d, find the ratio of their areas (in the same order).

⇒ Bases of the triangles = ax , bx

Similarly, it is given that ratio of altitudes is c : d

⇒ Altitudes of the triangle = cy , dy

Area of first triangle =

=

Area of second triangle =

Ratio of the areas of two triangle

=

=

Hence, ratio of area of two triangles is ac : bd

### The ratio of the bases of two triangles is a : b. If the ratio of their corresponding altitudes is c : d, find the ratio of their areas (in the same order).

⇒ Bases of the triangles = ax , bx

Similarly, it is given that ratio of altitudes is c : d

⇒ Altitudes of the triangle = cy , dy

Area of first triangle =

=

Area of second triangle =

Ratio of the areas of two triangle

=

=

Hence, ratio of area of two triangles is ac : bd

### The sides of triangle are 11 cm, 15 cm and 16 cm. What is the measure of altitude to the largest side?

⇒ Length of the side a = 3x , b = 4x and c = 5 x

Perimeter of the triangle = 144 m

3x + 4x + 5x = 144

12x = 144 ⇒ x = 12

Now Using Pythagoras theorem,

(5x)^{2} = (3x)^{2} + (4x)^{2}

25x^{2} = 9x^{2} + 16x^{2}

25x^{2} = 25x^{2} i.e. Pythagoras holds true

⇒ Given triangle is a right angled triangle

Base, b = 3x =3(12) = 36 m and Height, h = 4x =4(12) = 48 m

⇒ Area of the triangle =

### The sides of triangle are 11 cm, 15 cm and 16 cm. What is the measure of altitude to the largest side?

⇒ Length of the side a = 3x , b = 4x and c = 5 x

Perimeter of the triangle = 144 m

3x + 4x + 5x = 144

12x = 144 ⇒ x = 12

Now Using Pythagoras theorem,

(5x)^{2} = (3x)^{2} + (4x)^{2}

25x^{2} = 9x^{2} + 16x^{2}

25x^{2} = 25x^{2} i.e. Pythagoras holds true

⇒ Given triangle is a right angled triangle

Base, b = 3x =3(12) = 36 m and Height, h = 4x =4(12) = 48 m

⇒ Area of the triangle =

### The sides of triangle are 11 cm, 15 cm and 16 cm. What is the measure of altitude to the largest side?

Using Heron’s formula

Area of triangle = where s =

s = = 21

Area of triangle=

Since we have to find altitude to the largest side, base of the triangle = 16 cm

Also, area of triangle =

⇒

⇒ ( = 2.64)

Using Heron’s formula

Area of triangle = where s =

s = = 21

Area of triangle=

Since we have to find altitude to the largest side, base of the triangle = 16 cm

Also, area of triangle =

⇒

⇒ ( = 2.64)