**A-Level** **Mathematics**** Question Analysis Topic: Mathematics - Long Question**

**Exam Question:**

The sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.

**Answer:**

For A-Level Mathematics, you should know:

1) First, let's define a few variables:

**Let the sides of the first and second squares be x and y respectively**.

As such: area of first square = **x**^{2}, area of second square = **y**^{2}.

and perimeter of** first square = 4x**, **second square = 4y**

Let's start calculating!

**x2 + y2 = 400 ... (1)and 4x - 4y = 16 > 4(x - y) = 16 > x - y = 4 > x + y + 4 ... (2)**

Subbing y into (1), we get:

(y + 4)2 + y2 = 400

> y2 + 8y + 16 + y2 = 400

> 2y2 + 8y + 16 = 400

> 2(y2 + 4y + 8) = 400

> y2 + 4y + 8 = 200

> y2 + 16y - 12y - 192 = 0

> y(y + 16) - 12(y + 16) = 0

> **(y + 16)(y - 12) = 0**

> y + 16 = 0 or__ y = -16__ (impossible; how can a square's length be negative?)

and y = 12

Putting the value of y = 12 into (2):

x = 12 + 4 = 16

Hence, the sides are **12 **and **16cm** respectively.

Work hard for your A-Level Mathematics examination!

End of analysis. Great!