Question

The ratio of the areas of two triangles with common base in $4:3$. Height of the larger triangle is $20$ $cm$, then find the corresponding height of the smaller triangle

Answer 1

The ratio of the areas of two triangle with common base $=4:3$
Height of the larger triangle $\left(h_1\right)=20$ $cm$
Height of the smaller triangle $\left(h_2\right)=?$
$\frac{\text{Area of larger triangle}}{\text{Area of smaller triangle}}=\frac{h_1}{h_2}$ ....$[\because$ triangles have common base]
$\Rightarrow \frac{4}{3}=\frac{20}{h_2}$
$\Rightarrow h_2=\frac{3\times 20}{4}=15$ $cm$
$\therefore$ height of smaller triangle is $15$ $cm$.