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.

Assessment: WAEC SSCE - General Mathematics - 2001 (Essay) Subject: General Mathematics

Question 1 Report

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.

Answer

Answer Details

Sides \(x\) and \((x+7)\), diagonal \((x+8)\). By Pythagoras:

\(x^{2}+(x+7)^{2}=(x+8)^{2}\).

\(x^{2}+x^{2}+14x+49=x^{2}+16x+64\).

\(2x^{2}+14x+49-x^{2}-16x-64=0 \Rightarrow x^{2}-2x-15=0\).

\((x-5)(x+3)=0 \Rightarrow x=5\) (reject \(x=-3\), a length must be positive).

(a) \(x=5\ \text{m}\).

(b) Area \(=x(x+7)=5\times 12=\mathbf{60\ m^{2}}\).

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