Question

The area of a right-angled triangle is 165 sq metres. Then, find its base and altitude if the latter exceeds the former by 7 meters?

• A. 16 m and 24 m
• B. 14 m and 22 m
• C. 15 m and 22 m
• D. 16 m and 20 m

Answer 1

The correct option is C

15 m and 22 m

Let base = x then, altitude x + 7
$\therefore Area\frac{1}{2}\times x\times (x+7)\therefore 165=\frac{x(x+7)}{2}\Rightarrow 330=x^2+7x\Rightarrow x^2+7x-330=0(x+22)(x-15)=0\Rightarrow x=-22andn=15\therefore baseisx=15mAltitudex+7=22m$