In the given figure, DE || BC. If DE = 3 cm, BC = 6 cm and ar (ΔADE) = 15 cm², find the area of ΔABC.

Question

In the given figure, DE || BC. If DE = 3 cm, BC = 6 cm and ar (ΔADE) = 15 cm 2 , find the area of ΔABC.

Philoid · Accepted Answer

It is given that DE || BC

∴∠ ADE = ∠ ABC (Corresponding angles)

∠ AED = ∠ ACB (Corresponding angles)

So, by AA similarity criterion ΔADE ~ 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.

Hence, proved.

In the given figure, DE || BC. If DE = 3 cm, BC = 6 cm and ar (ΔADE) = 15 cm2, find the area of ΔABC.