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!