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Square ABCD has an area of 9 square inches. Sides AD

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by VJesus12 » Sun Apr 14, 2019 9:30 am

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Square ABCD has an area of 9 square inches. Sides AD and BC are lengthened to x inches each. By how many inches were sides AD and BC lengthened?

(1) The diagonal of the resulting rectangle measures 5 inches.
(2) The resulting rectangle can be cut into three rectangles of equal size.

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT
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Source: — Data Sufficiency |

by Vincen » Sat Apr 20, 2019 5:31 am
Image

Square ABCD has an area of 9 square inches. Sides AD and BC are lengthened to x inches each. By how many inches were sides AD and BC lengthened?

(1) The diagonal of the resulting rectangle measures 5 inches.
(2) The resulting rectangle can be cut into three rectangles of equal size.

OA=A

Source: Manhattan GMAT
Hi Vjesus12.

Here, the question we need to answer is, what is \(x\)?

Statement 1:
(1) The diagonal of the resulting rectangle measures 5 inches.
Since the square has an area of 9 square inches, then AB=BC=3 in. Then, we can draw the following picture
Image

By the Pythagorean Theorem, we get that $$\left(3+x\right)^2+3^2=5$$ and from this equation we can get the value of \( x\). So, this statement is SUFFICIENT.

Statement 2:
(2) The resulting rectangle can be cut into three rectangles of equal size.
This information doesn't tell us anything since any rectangle can be divided into 3 rectangles of equal size. So, this statement is NOT SUFFICIENT.

Therefore, the correct answer is the option _A_.

I hope it helps you.
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