Question

The area of a right-angle triangle is 165 m². Determine its base and altitude if the latter exceeds the former by 7 metres.

Answer 1

$$\begin{gathered} \text{Let the base of the right-angled triangle be}x\text{cm.} \\ \mathrm{According}\mathrm{to}\mathrm{the}\mathrm{question}: \\ \text{Altitude =}(x+7)\text{cm} \\ \therefore \mathrm{A}\text{rea of the triangle =}\frac{1}{2}\times x\times (x+7){\text{cm}}^2 \\ \mathrm{Now}\text{,} \\ \frac{1}{2}\times x\times (x+7)=165 \\ \text{⇒}{x}^2+7x-330=0 \\ \text{⇒}{x}^2+(22-15)x-330=0 \\ \text{⇒}{x}^2+22x-15x-330=0 \\ \text{⇒}x(x+22)-15(x+22)=0 \\ \Rightarrow (x+22)(x-15)=0 \\ \therefore x=-22,x=15 \\ \text{The base of the triangle can never be negative.} \\ \text{Therefore, the base of the right-angled triangle is 15 cm.} \\ \mathrm{Altitude}=(15+7)=22\mathrm{cm} \end{gathered}$$