Question

In the given figure, if $$\angle ADE = \angle B$$, show that $$\Delta ADE \sim \Delta ABC$$. If $$AD = 3.8 cm, AE = 3.6 cm, BE = 2.1 cm$$ and $$BC = 4.2 cm$$, find $$DE$$.

Answer 1

From given figure,

$$\angle ADE = \angle B$$

To prove: $$\Delta ADE \sim \Delta ABC$$ and

find $$DE$$

Given: $$AD = 3.8 cm, \ AE = 3.6 cm, \ BE = 2.1 cm$$ and $$BC = 4.2 cm$$

Now, In $$\Delta ADE$$ and $$\Delta ABC$$

$$\angle ADE = \angle B$$ (given)

$$\angle A = \angle A$$ (common)

$$\Delta ADE \sim \Delta ABC$$ (By AA)

Again,

$$\dfrac{AD}{AB} = \dfrac{DE}{BC}$$

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

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

$$\dfrac{3.8}{5.4} = \dfrac{x}{4.2}$$

$$x = 2.8$$

$$DE = 2.8cm$$