Question

The area of the triangle is $216c{m}^2.$One triangle measures is $24cm$. Find the distance of the corresponding vertex from the side.

Answer 1

Finding the distance of the corresponding vertex from the side:

Given the area of the triangle is $216c{m}^2.$One triangle measures is $24cm$(base)

Area of the right angles triangle =$\frac{1}{2}\times b\times h\mathrm{where}\mathrm{b}\mathrm{is}\mathrm{the}\mathrm{base}\mathrm{and}\mathrm{height}\mathrm{is}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{triangle}.$

$$\begin{gathered} 216=\frac{1}{2}\times 24\times h(\mathrm{h}\mathrm{is}\mathrm{the}\mathrm{distance}\mathrm{of}\mathrm{the}\mathrm{corresponding}\mathrm{vertex}\mathrm{from}\mathrm{the}\mathrm{side}.) \\ h=\frac{216\times 2}{24} \\ h=9\times 2 \\ h=18cm. \end{gathered}$$

Hence, the height of the triangle is $18cm.$