Question

The sides of a rectangular object floor are × m and (×+7) m. The diagonal is (×+8) m, calculate, in metres:
i. the value of ×
ii. the area of the floor

Answer 1

Answer:

Using Pythagoras Theorem

x^2 + (x + 7)^2 = (x + 8)^2

x^2 + x^2 + 14x + 49 = x^2 + 16x + 64

Collect like terms:

x^2 + x^2 - x^2 + 14x - 16x + 49 - 64 = 0

x^2 - 2x - 15 = 0

Factorise

(x + 3)(x - 5) = 0

x + 3 = 0

x = -3 (Disregard as -ve value)

x - 5 = 0

x = 5.

Area of floor will be x(x + 7)

= 5(5 + 7)

= 60 m^2