Maths-

General

Easy

Question

# A square and equilateral triangle have equal perimeters. If the diagonal of the square is 12 cm, find the area of triangle.

Hint:

### Use Pythagoras theorem to find side of the square.

## The correct answer is: 110.85 cm2

### It is given that diagonal of the square = 12 cm

Using Pythagoras theorem in triangle ACD

AD^{2} = AC^{2} + CD^{2}

(12)^{2} = x^{2} + x^{2} = 2x^{2}

288 = 2x^{2}

144 = x^{2}

12 = x

So, side of the square = 12 cm

Let side of an equilateral triangle = a

Perimeter of triangle = Perimeter of square

⇒ 3a = 4(side) = 4(12) = 48 cm

⇒ a = 16 cm

Now, Area of an equilateral triangle = a^{2}

= 16^{2} = 64

( = 1.73)

= 110.85 cm^{2}

### Related Questions to study

Maths-

### Identify a line with an undefined slope .Application

a. y = x

b. y+ x =0

c. y = 10

d. x = 1

### Identify a line with an undefined slope .Application

a. y = x

b. y+ x =0

c. y = 10

d. x = 1

Maths-General

Maths-

### The lengths of the two sides of right triangle containing the right angle differ by 2 cm. If the area of triangle is 24 cm^{2}. Find the perimeter of triangle

### The lengths of the two sides of right triangle containing the right angle differ by 2 cm. If the area of triangle is 24 cm^{2}. Find the perimeter of triangle

Maths-General

Maths-

### Identify a line having zero slope. Application

a. x = y

b. x = 100

c. y = 100

d. x = 0

### Identify a line having zero slope. Application

a. x = y

b. x = 100

c. y = 100

d. x = 0

Maths-General

Maths-

### The cost of an ice cream scoop is $11 and the cost of additional toppings is $1.50. Find the cost of an ice cream with 4 toppings.

### The cost of an ice cream scoop is $11 and the cost of additional toppings is $1.50. Find the cost of an ice cream with 4 toppings.

Maths-General

Maths-

### The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up when writing 310 words on an average. How many words would use up a bottle of ink containing one fifth of litre?

### The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up when writing 310 words on an average. How many words would use up a bottle of ink containing one fifth of litre?

Maths-General

Maths-

### Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.Application

### Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.Application

Maths-General

Maths-

### Identify the parallel lines and perpendicular lines from the given set. Application

2x + y = 1

9x + 3y = 6

y = 3x

y = -3x

2y = 4x +6

Y = - x/2

### Identify the parallel lines and perpendicular lines from the given set. Application

2x + y = 1

9x + 3y = 6

y = 3x

y = -3x

2y = 4x +6

Y = - x/2

Maths-General

Maths-

### A line l touches the Y-axis at point 3 and has slope –3. Find the slope of the line perpendicular to the line l.

### A line l touches the Y-axis at point 3 and has slope –3. Find the slope of the line perpendicular to the line l.

Maths-General

Maths-

### Identify the equation of a line parallel to the line y = x – 1

### Identify the equation of a line parallel to the line y = x – 1

Maths-General

Maths-

### The sum of the radius and height of a cylinder is 21 cm and the T.S.A of the cylinder is 660 sq. cm. Find the height and volume of the cylinder?

### The sum of the radius and height of a cylinder is 21 cm and the T.S.A of the cylinder is 660 sq. cm. Find the height and volume of the cylinder?

Maths-General

Maths-

### Identify the equation of a line perpendicular to the line x/2 + y = -1

### Identify the equation of a line perpendicular to the line x/2 + y = -1

Maths-General

Maths-

### A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis? Application

### A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis? Application

Maths-General

Maths-

### Find the equation of a line which passes through (1, 2) and is perpendicular to the line with an equation y = x – 1.

### Find the equation of a line which passes through (1, 2) and is perpendicular to the line with an equation y = x – 1.

Maths-General

Maths-

### Find the equation of line such that its y-intercept is 20 and slope is ½.Application

### Find the equation of line such that its y-intercept is 20 and slope is ½.Application

Maths-General

Maths-

### Identify the line having y-intercept = 1/2

### Identify the line having y-intercept = 1/2

Maths-General