Question

The area of a right angled triangle is 165 $m^2$. Determine its base ___m if the altitude exceeds the base by 7m.

Answer 1

$\Rightarrow$ Let base of right angled triangle be $xm$

$\Rightarrow$ Then, altitude of right angled triangle becomes $(x+7)m$

$\Rightarrow$ Area of right angled triangle $=165m^2$

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

$\Rightarrow$ $x^2+7x=330$

$\Rightarrow$ $x^2+7x-330=0$

$\Rightarrow$ $x^2+22x-15x-330=0$

$\Rightarrow$ $x(x+22)-15(x+22)=0$

$\Rightarrow$ $(x+22)(x-15)=0$

$\therefore$ $x=-22$ and $x=15$

Base cannot be negative.

$\therefore$ Base of right angled triangle is $15m$