Question

The ratio of the areas of two triangles with the common base is $8:7$. Height of the larger triangle is $4\text{cm}$, then find the corresponding height of the smaller triangle.

Answer 1

The ratio of the areas of two triangle with common base $A_1:A_2=8:7$
Height of the larger triangle $\left(h_1\right)=4\text{cm}$
Height of the smaller triangle $\left(h_2\right)=?$

$\frac{\text{Area of larger triangle}}{\text{Area of smaller triangle}}=\frac{b_1\times h_1}{b_2\times h_2}$

$\frac{8}{7}=\frac{4}{h_2}$

$h_2=\frac{7\times 4}{8}\text{cm}$

$=3.5\text{cm}$

Hence, the corresponding height of the smaller triangle is $3.5\text{cm}$.