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

Question

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 .

littlewarthog · Answer

To answer that question, we can assume a very easy triangle and use it as it as an example.

Let's take a right isosceles triangle with the two equal sides a and b. The area is

\frac{1}{2}*a*b=\frac{1}{2}a^2

If the two sides a and b are increased by 40%, we get:

\frac{1}{2}*1.4 a*1.4 a=1.96*\frac{1}{2}*a^2

So the are is 1.96 times the size it was before, so it increased by 96%. Answer D.

g106 · Answer

The area is 1/2 * b * h

if all the sides increased by 40%

then the area = 1/2 * 1.4b * 1.4 h = 1.96 / 2 * b * h
 = 1.96 (1/2 * b * h)
 so the % increase will be 96

Ans D 96%

PareshGmat · Answer

Answer = D. 96%

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

Bunuel · Answer

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.

ScottTargetTestPrep · Answer

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%

Answer: D

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

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