Box surrounded with squares

Geometry Level 2

In the figure shown there is a yellow rectangle that is surrounded by squares of different sizes.

If the smaller side of the yellow rectangle measures 40 cm, what is the length of its larger side?

50 cm 60 cm 54 cm 42 cm 48 cm

1 solution

Stephen Mellor
Dec 6, 2017

Let the side length of the green squares be $x$ and the side length of the blue squares be $y$ .

We can get the width from left to right of the entire figure in 2 ways, and can derive 2 expressions which therefore must be equal.

$9y = 6y + 2x$

or,

$6y = 4x$ .

We can see that the shorter side of the yellow rectangle is equal to $4x - y$

Therefore, $4x - y = 40$

Substituting in, $6y - y = 40$

or, $5y = 40$

hence, $y = 8$

As the length of the yellow rectangle is $6y = \boxed{48}$ , this is the answer.