Question

$\Delta$ABC is an isosceles tringle in which AB$=$AC. D and E are the midpoints of sides AB and AC and DE$=3.5$cm. Find the perimeter of $\Delta$ABC when AD$=4.5$cm.

Answer 1

AD$=$DB$=4.5$cm [midpoint]

In $\Delta ABC$ & $\Delta ADE$

$\angle A=\angle A$ [common angle]

$\frac{AB}{AD}=\frac{AC}{AE}=2$

$\therefore$ By SAS property of triangles $\Delta ABC\sim \Delta ADE$

$\frac{AB}{AD}=\frac{BC}{DE}=2$

So $BC=2\times DE$

$=2\times 3.5=7$

Perimeter of $\Delta ABC=4.5+4.5+7=4.5+4.5$

$=9+7+9$

$=25$cm.