Question

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

Answer 1

Let the base and altitude be x and x+7 respectively.

Area of triangle = $\frac{1}{2}\times base\times height$

$165=\frac{1}{2}\times x\times (x+7)$

$330=x(x+7)$
$x^2+7x-330=0$
$(x-15)(x+20)=0$

$x=15orx=-20$ (rejected because it is negative)

So, x = 15
And,x + 7 = 22

So the base and height are 15m and 22m respectively.