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