Question

Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of corresponding heights is :

• A. 4: 5
• B. 5: 4
• C. 3: 2
• D. 5: 7

Answer 1

The correct option is A

4: 5

For similar triangles,

$\frac{Areaof1st}{Areaof2nd}$ = $\frac{(Correspondinglengthof1st{)}^2}{(Correspondinglengthof2nd{)}^2}$

$\frac{Area\left({\Delta }_1\right)}{Area\left({\Delta }_2\right)}=\frac{(h_1{)}^2}{(h_2{)}^2}$

$\frac{16}{25}=\frac{(h_1{)}^2}{(h_2{)}^2}$

$\frac{h_1}{h_2}=\frac{4}{5}$