Question

In the given figure, if ∠ADE = ∠B, AD = 3.8 cm, AE = 3.6 cm, BE = 2.1 cm and BC = 4.2 cm, find DE.

• A. 3.6 cm
• B. 4.7 cm
• C. 2.8 cm
• D. 5.2 cm

Answer 1

The correct option is C 2.8 cm

Given:
∠ADE = ∠B
AD = 3.8 cm, AE = 3.6 cm,
BE = 2.1 cm and BC = 4.2 cm

Let length of DE be x.

Now, in ∆ADE and ∆ABC,

∠ADE = ∠B (given)

∠A = ∠A (common)

$\therefore$ ∆ADE $\sim$ ∆ABC (AA similarity criterion)

$\Rightarrow$ $\frac{AD}{AB}=\frac{DE}{BC}$
(corresponding sides of similar triangle are in same ratio)

$\frac{AD}{AE+EB}=\frac{x}{4.2}$

$\frac{3.8}{3.6+2.1}=\frac{x}{4.2}$

$\frac{3.8}{5.7}=\frac{x}{4.2}$

x = 2.8

$\Rightarrow$ DE = 2.8 cm