Question

If triangle ABC is an isosceles triangle in which AB = AC = 13 cm then find the value of $\frac{\text{area of}\Delta ADC}{\text{area of}\Delta EFB}.$

Answer 1

In $\Delta ADC$ and $\Delta FEB,$

$\angle C=\angle B$

(since base angles of isosceles triangle are equal)

$\angle ADC=\angle EFG={90}^{\circ }$

$\therefore \Delta ADC\sim \Delta EFB$ (by AA similarity criterion) (1 mark)

$\Rightarrow \frac{\text{area of}\Delta ADC}{\text{area of}\Delta EFB}=\frac{A{C}^2}{B{E}^2}=\frac{A{C}^2}{(BC+CE{)}^2}$ (1 mark)

(The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides)

$\Rightarrow \frac{\text{area of}\Delta ADC}{\text{area of}\Delta EFB}=\frac{(13{)}^2}{(10+8{)}^2}$

$=\frac{(13{)}^2}{(18{)}^2}=\frac{169}{324}$ (1 mark)