A square inside a square

Geometry Level 2

A square is inside a square. The green region has a uniform width and has an area of $14.6~cm^2$ . The length of each side of the red square is $6.8~cm$ . What is the length of each side of the bigger square in $inches$ ?

Note: Use $1~inch = 2.5~cm$

The answer is 3.12.

1 solution

A Former Brilliant Member
Apr 2, 2017

let $x$ be the side length of the big square

$\text{area of the green region = area of the big square - area of the red square}$

$14.6 = x^2 - 6.8^2$ $\implies$ $x = 7.8~cm$

Converting $cm$ to $inches$ , we have

$7.8~cm$ $\large(\dfrac{1~inch}{2.5~cm})$ $=$ $\boxed{\large\color{#D61F06}3.12~inches}$

A square inside a square

The answer is 3.12.

1 solution

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