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

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

Let the base be $x \mathrm{~m}$ .

Therefore, the altitude will be $(x+7) m$ .

Area of a triangle $=\frac{1}{2} \times$ Base $\times$ Altitude

$\begin{array}{l} \therefore \frac{1}{2} \times x \times(x+7)=165 \\ \Rightarrow x^{2}+7 x=330 \\ \Rightarrow x^{2}+7 x-330=0 \end{array}$
$\begin{array}{l} \Rightarrow x^{2}+(22-15) x-330=0 \\ \Rightarrow x^{2}+22 x-15 x-330=0 \\ \Rightarrow x(x+22)-15(x+22)=0 \\ \Rightarrow(x+22)(x-15)=0 \\ \Rightarrow x=-22 \text { or } x=15 \end{array}$