Question

The area of a triangle is equal to that of square of side $60cm$. Find the side of a triangle whose corresponding altitude is $90cm$.

Answer 1

Given the side of square$=60cm$

Step 1: Area of a square

$$\begin{gathered} =side\times side \\ =60\times 60 \\ =3600c{m}^2 \end{gathered}$$

Given the area of a triangle is equal to the area of a square

so, the area of a triangle $=3600c{m}^2$

Step 2: Area of a triangle

Given the altitude of a triangle $=90cm$

We know the area of a triangle$=\frac{1}{2}\times base\times altitude$

$$\begin{gathered} \Rightarrow 3600=\frac{1}{2}\times base\times 90 \\ \Rightarrow 3600=45\times base \\ \Rightarrow base=\frac{3600}{45} \\ \Rightarrow base=80cm \end{gathered}$$

Hence, the side of a triangle is$80cm$