Question

# The difference between the sides at right angles in right angled triangle is 14 cm. The area of triangle is 120 cm^{2} . Calculate the perimeter of triangle

Hint:

### Sides containing right angle are height and base.

## The correct answer is: 60 cm

### It is given that difference between perpendicular and base = 14 cm

i.e. b – h = 14 ⇒ b = 14 + h

Now, Area of triangle = 120 cm^{2}

= 120

= 240

h^{2} + 14h – 240 = 0

h =

h =

h = 10 , - 24

Since, perpendicular is always positive so h = 10

Base, B = 14 + 10 = 24

Using Pythagoras theorem ,

H^{2} = B^{2} + P^{2}

H^{2} = 24^{2} + 10^{2} = 576 + 100 = 676

H = = 26 cm

Perimeter of triangle = Sum of all sides

= 24 + 10 + 26 = 60 cm

### Related Questions to study

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**Note:**

There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage. When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).

Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.

Carrie redesigned the container because the initial sketch did not account for cushioning material between the glasses. The area of the base of the newly designed container is greater than the area of the base in the initial sketch. What is the area, in square inches, of the base of the newly designed container?

**Note:**

There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage. When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).

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**Note:**

Another answer for this problem could be taken as 137 as well.

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