Theory question 103
Quadratic EquationsThe 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.
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Model answer
(a) Pythagoras: x2 + (x + 7)2 = (x + 8)2, so 2x2 + 14x + 49 = x2 + 16x + 64.
x2 − 2x − 15 = 0, (x − 5)(x + 3) = 0, x = 5 (a length is positive).
(b) Area = 5 × 12 = 60 m2.
Explanation
The diagonal is the hypotenuse of the right-angled triangle formed by two sides.