Question

10. In the figure, if AABC - AADE, then the length of BC is: (a) 3 cm (b) 3.2 cm (c) 3.9 cm (d) 4.5 cm с 4 E 1.5 2. A B D​

Answer 1

Given: ΔABC≈ΔADE

To Find

The length of line segment BC.

Solution:

ΔABC≈ΔADE (given)

So, the sides of the two similar triangles are proportional to each other

                ⇒ $\frac{BC}{DE}$ = $\frac{AC}{AE}$

                ⇒ $\frac{BC}{DE} = \frac{AE+EC}{AE}$

                ⇒ BC= $\frac{(AE+EC)DE}{AE}$

               ⇒ BC= $\frac{(2+4)1.5}{2}$

               ⇒ BC= $\frac{6+1.5}{2}$

               ⇒ BC= 4.5 cm

Therefore, the length of BC is option(d). 4.5 cm.