In Fig, DE || BC, If DE = 4 m, BC = 6 cm and Area (ΔADE) = 16 cm2, f

1.	In Fig, DE \|\| BC, If DE = 4 m, BC = 6 cm and Area (ΔADE) = 16 cm2, find the area of ΔABC.
Answer» Given, DE ∥ BC. In ΔADE and ΔABC We know that, ∠ADE = ∠B [Corresponding angles] ∠DAE = ∠BAC [Common] Hence, ΔADE ~ ΔABC (AA Similarity) Since the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides, we have, \(\frac{Ar(ΔADE)}{Ar(ΔABC)}\) = \(\frac{DE^2}{BC^2}\) \(\frac{16}{Ar(ΔABC)}\) = \(\frac{42}{62}\) ⇒ Ar(ΔABC) = \(\frac{(62 \times 16)}{42}\) ⇒ Ar(ΔABC) = 36 cm²

In Fig, DE || BC, If DE = 4 m, BC = 6 cm and Area (ΔADE) = 16 cm2, find the area of ΔABC.

Answer»

Given,

DE ∥ BC.

In ΔADE and ΔABC

We know that,

∠ADE = ∠B [Corresponding angles]

∠DAE = ∠BAC [Common]

Hence, ΔADE ~ ΔABC (AA Similarity)

Since the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides, we have,

\(\frac{Ar(ΔADE)}{Ar(ΔABC)}\) = \(\frac{DE^2}{BC^2}\)

\(\frac{16}{Ar(ΔABC)}\) = \(\frac{42}{62}\)

⇒ Ar(ΔABC) = \(\frac{(62 \times 16)}{42}\)

⇒ Ar(ΔABC) = 36 cm²