In the given figure, $D E | | B C$ and $D E : B C = 3 : 5$ . Calculate: $a r (△ A D E) : a r (t r a p B C E D)$ .

Open in App

Solution

In $Δ A D E$ and $Δ A B C$
$∠ A D E = ∠ A B C$ (corresponding angle)
$∠ A E D = ∠ A C B$ (corresponding angle)
So, $Δ A D E \sim Δ A B C$ (by AA similarity criterion)
$\frac{a r (A D E)}{a r (A B C)} = (\frac{D E}{B C})^{2}$

$= (\frac{3}{5})^{2} = \frac{9}{25}$

$\frac{a r (A B C)}{a r (A D E)} = \frac{25}{9}$

$\frac{a r (A B C)}{a r (A D E)} = \frac{25}{9}$

$\frac{a r (A B C)}{a r (A D E)} - 1 = \frac{25}{9} - 1$

$\frac{a r (A B C) - a r (A B C)}{a r (A D E)} = \frac{16}{9}$

$\frac{a r (B C E D)}{a r (A D E)} = \frac{16}{9}$

$\frac{a r (A D E)}{a r (B C E D)} = \frac{9}{16}$

$a r (A D E) : a r (B C E D) = 9 : 16$

Suggest Corrections

Similar questions

D E | | B C

D E : B C = 3 : 5

A (△ A D E) : A (D B C E)

In the given fig ure, DE ∥ BC . (i) If DE = 4 cm, BC = 8 cm and A (△ ADE) = 25 {cm}^{2}, find A (△ ABC) . (ii) If DE : BC = 3 : 5, then find A (△ ADE) : A (□ DBCE) .

In the adjoining figure, DE ∥ BC and AD : DB = 5 : 4 . Find (i) DE : BC (ii) DO : DC (iii) A (△ DOE) : A (△ DCE)

In the given figure, DE || BC and DE : BC = 3 : 5. Calculate the ratio of the areas of $Δ A D E$ and the trapezium BCED.

Join BYJU'S Learning Program