Question

A rectangle has side lengths of x cm and (x + y) cm, where x and y are

both positive.
The rectangle has an area of 54 cm² and a perimeter of 42 cm.
Work out the values of x and y.

Answer 1

x(x + y) = 54

2(x + x + y) = 42

x² + xy = 54

2x + y = 21----->y = 21 - 2x

x² + x(21 - 2x) = 54

x² + 21x - 2x² = 54

21x - x² = 54

x² - 21x + 54 = 0

(x - 3)(x - 18) = 0

x = 3, 18

x = 3 and y = 18, or x = 18 and y = 3