Question

The ratio of the areas of two triangles of the same height is equal to the ratio of their bases.

• A. True
• B. False

Answer 1

The correct option is A True

To prove: The ratio of the areas of two triangles of the same height is equal to the ratio of their bases.

Proof:
Let us take triangle $T_1$ with height $h_1$ and base $b_1$ and Triangle $T_2$ with height $h_2$ and base $b_2$.

It is also given that height of the two triangles is equal so, we can consider that $h_1=h_2=h$.
$\begin{array}{cc}\text{Area of Triangle}{T}_1& =\frac{1}{2}\times base\times height\\ & =\frac{1}{2}\times b_1\times h_1\end{array}$

$\begin{array}{cc}\text{Area of Triangle}{T}_2& =\frac{1}{2}\times base\times height\\ & =\frac{1}{2}\times b_2\times h_2\end{array}$

Now, the ratio of area of two triangles is,
$\begin{array}{cc}\frac{\text{Area of triangle}{T}_1}{\text{Area of triangle}{T}_2}& =\frac{\frac{1}{2}\times b_1\times h_1}{\frac{1}{2}\times b_2\times h_2}\\ & =\frac{b_1\times h}{b_2\times h}\\ & =\frac{b_1}{b_2}\end{array}$
Hence, proved.