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# If the length of each of the sides of three square garden plots is inc

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Math Expert
Joined: 02 Sep 2009
Posts: 44423
If the length of each of the sides of three square garden plots is inc [#permalink]

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26 Sep 2017, 00:26
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If the length of each of the sides of three square garden plots is increased by 50%, by what percent is the sum of the areas of the three plots increased?

(A) 375%
(B) 200%
(C) 150%
(D) 125%
(E) 50%
[Reveal] Spoiler: OA

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If the length of each of the sides of three square garden plots is inc [#permalink]

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26 Sep 2017, 00:42
If the length of each of the sides of three square garden plots is increased by 50%, by what percent is the sum of the areas of the three plots increased?

Let the length of each of the three square garden plots is 10 units
Since the lengths are increase by 50%, the new lengths are 15 units each.

The sum of the areas of the three square plots was 3(10^2) = 300

Now, the sum of the areas must be 3(15^2) = 3(225) = 675

This represents an increase of 675 - 300 = 375, which is an increase of $$\frac{375}{300}*100 = \frac{5}{4}*100 = 125%$$(Option D)
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If the length of each of the sides of three square garden plots is inc [#permalink]

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26 Sep 2017, 09:17
Bunuel wrote:
If the length of each of the sides of three square garden plots is increased by 50%, by what percent is the sum of the areas of the three plots increased?

(A) 375%
(B) 200%
(C) 150%
(D) 125%
(E) 50%

Use one square

Areas all increase identically. Percent increase from 3 areas summed, to sum of areas' increases, is not different from percent increase of one area to one area increased.

Use one square.

Original area = $$s^2$$ = x

Each length is increased by 50%, so

New area is
(1.5s)(1.5s) =
2.25$$s^2$$, $$s^2$$ = x

New area: 2.25x

By what percent did area increase?

$$\frac{new - old}{old} * 100$$

Percent increase:

$$\frac{2.25x - x}{x}$$ =$$\frac{1.25x}{x} = 1.25 * 100 = 125$$%

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If the length of each of the sides of three square garden plots is inc   [#permalink] 26 Sep 2017, 09:17
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