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A-Level Mathematics Question Analysis - Mathematics - Long Question

A-Level Mathematics Question Analysis

· A-Level Maths,alevel mathematics,simultaneous eq

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 = x2, area of second square = y2.

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!

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