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# If all the sides of a right triangle increase in length by 40%, then

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Re: If all the sides of a right triangle increase in length by 40%, then [#permalink]
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Let initial base & height = 100 each

Area $$= \frac{1}{2} * 100 * 100$$

Post increase of 40% in dimensions, area $$= \frac{1}{2} * 140 * 140$$

Increase % $$= \frac{\frac{1}{2} * 140 * 140 - \frac{1}{2} * 100 * 100}{\frac{1}{2} * 100 * 100} * 100 = 196 - 100 = 96$$
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Re: If all the sides of a right triangle increase in length by 40%, then [#permalink]
Bunuel wrote:

Tough and Tricky questions: Geometry.

If all the sides of a right triangle increase in length by 40%, then by what percentage does the area of the triangle increase?

A. 16%
B. 40%
C. 80%
D. 96%
E. 120%

Kudos for a correct solution.

OFFICIAL SOLUTION:

(D) Let the base and height be b and h respectively, before they are increased. After the increase, the base and height are 1.4b and 1.4h respectively.

Area of a Triangle = (1/2)(base)(height).
Area before the increase = (1/2)bh.
Area after the increase = (1/2)(1.4b)(1.4h)= (1/2)(1.96bh)= (1.96)((1/2)bh).

The percent increase in area is:
((Change in Area)/(Original Area)) × 100%= ((1/2)(1.96bh) – (1/2)bh)/((1/2)bh))=1.96 – 1 = .96= 96%.

The correct answer is choice (D).

Note: This would also be a very good question to use number plugin.
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Re: If all the sides of a right triangle increase in length by 40%, then [#permalink]
Bunuel wrote:

Tough and Tricky questions: Geometry.

If all the sides of a right triangle increase in length by 40%, then by what percentage does the area of the triangle increase?

A. 16%
B. 40%
C. 80%
D. 96%
E. 120%

Let’s say the initial base and height of the triangle are 10 and 10, respectively. So the area is (10 x 10)/2 = 50.

If all the sides are increased by 40%, then the new base and height are 14 and 14, respectively. So the area of the enlarged triangle is (14 x 14)/2 = 98.

So the percent increase is:

(98 - 50)/50 x 100

48/50 x 100 = 96%