AAPL wrote: ↑

Wed May 31, 2023 8:46 am

Official Guide

153y8e8.png

In the quilting pattern shown above, a small square has its vertices on the sides of a larger square. What is the side length, in centimeters, of the larger square?

1) The side length of the smaller square is \(10\,\text{cm}\)

2) Each vertex of the small square cuts \(1\) side of the larger square into \(2\) segments with lengths in the ratio \(1:2\)

OA C

There is one unknown, that is the side of the larger square.
We need something that gives us the side of the bigger square that is in either a variable form which could be determined or in a direct value form.

Statement 1 does not have any relation to side of bigger square, hence insufficient. \(\Large{\color{red}\chi}\)

Statement 2 gives a variable relation as, if the side of the bigger square is \(3x\), then the triangles whose hypotenuse is given by Statement 1 has sides \(2x\) and \(x\) which gives an equation to determine \(x (4x^2 + X^2 = 10^2)\). \(\Large{\color{red}\chi}\)

Therefore, both statements are required together to arrive at a definite answer, which means, the correct answer is C