Question

What will be the percentage change in the area of a right angle triangle with base 40 cm and height 30 cm, when the base is increased by 30% and height is increased by 40%?
1. 35%
2. 70%
3. 78%
4. 82%

Answer 1

Correct Answer - Option 4 : 82%

Concept:

Area of right triangle = \({\frac{1}{2}}\) × base × height

Calculation:

Given:

In right triangle, base = 40 cm and height = 30 cm

Area = \({\frac{1}{2}}\) × base × height

Area = \({\frac{1}{2}}\) × 40 × 30

Area = 600 cm²

Now, after increasing the base by 30%,

base = 40 × 1.3 cm

base = 52 cm

Now, after increasing the height by 40%,

height = 30 × 1.4 cm

height = 42 cm

Area = \({\frac{1}{2}}\) × 52 × 42

Area = 1092 cm²

Change in area = (Final area) - (Initial area)

Change in area = (1092 - 600) cm²

Change in area = 492 cm².

The percentage change in the area = \(\frac{492\times100}{600} \%\)

The percentage change in the area = 82%

Hence the required change in the area of the triangle is 82%.