Question

In two triangle, the ratio of their areas is 4:3 and that heights is 3:4 find the ratio of their bases

Answer 1

let the two triangle have

bases $b_1,b_2$ and heights $h_1,h_2$

ratio of their areas $=\frac{\frac{1}{2}\times b_1{h}_1}{\frac{1}{2}\times b_2{h}_2}=\frac{b_1{h}_1}{b_2{h}_2}$

But given ratio of areas $=\frac{4}{3}$ and $\frac{h_1}{h_2}=\frac{3}{4}$

$\frac{b_1{h}_1}{b_2{h}_2}=\frac{4}{3}\Rightarrow \frac{b_1}{b_2}\times \frac{3}{4}=\frac{4}{3}$

$\Rightarrow \frac{b_1}{b_2}=\frac{16}{9}$