Question

The ratio of the areas of two triangles with the equal base is $6:5$. If the height of the bigger triangle is $9cm$, then find corresponding height of the smaller triangle.

Answer 1

Let $A_1$ and $A_2$ be the areas of the two triangles respectively.

$A_1>A_2$

$A_1=\frac{1}{2}{b}_1{h}_1$ and $A_2=\frac{1}{2}{b}_2{h}_2$

$\frac{A_1}{A_2}=\frac{\frac{1}{2}{b}_1{h}_1}{\frac{1}{2}{b}_2{h}_2}$

$\frac{6}{5}=\frac{b_1{h}_1}{b_2{h}_2}$

Given that $b_1=b_2$

$\Rightarrow \frac{h_1}{h_2}=\frac{6}{5}$

Given $h_1=9$cm

$\Rightarrow \frac{9}{h_2}=\frac{6}{5}$

$\Rightarrow h_2=\frac{9\times 5}{6}=\frac{45}{6}=7.5$cm

thus, height of the smaller triangle$=7.5$cm