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

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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

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