ΔABC is right-angled at A and AD ⊥ BC. If BC = 13 cm and AC = 5 cm, find the ratio of the areas of ΔABC and ΔADC.

Question

Philoid · Accepted Answer

In ΔABC and ΔADC

∴∠ BAC = ∠ ADC (90° angle)

∠ ACB = ∠ ACD (Common)

So, by AA similarity criterion ΔADC ~ ΔABC

We know that if two triangles are similar then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.