The sides of a rectangular floor are xm and (x + 7)m. The diagonal is (x + 8)m. Calculate, in metres :
(a) the value of x ;
(b) the area of the floor.
Explanation
(a)
((x + 8)^{2} = x^{2} + (x + 7)^{2})
(x^{2} + 16x + 64 = x^{2} + x^{2} + 14x + 49)
(x^{2} + 16x + 64 – 2x^{2} – 14x – 49 = 0)
(15 + 2x – x^{2} = 0)
(x^{2} – 2x – 15 = 0)
((x + 3)(x – 5) = 0)
x = 5m since measurements cannot be negative.
(b) (Area = length times breadth)
Length = (x + 7) = (5 + 7) = 12 m
Breadth = x m = 5 m
(Area = 12 times 5 = 60 m^{2})