Question

In Fig. 7, if A ABC ~ A DEF and their sides of lengths (in cm) are marked
along them, then find the lengths of sides of each triangle.​

Answer 1

AB = 9 cm

BC = 12 cm

CA = 15 cm

DE = 18 cm

EF = 24 cm

FD = 30 cm

Step-by-step explanation:

We have Δ ABC and Δ DEF are similar.

Hence, $\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}$

So, $\frac{2x - 1}{18} = \frac{3x}{6x}$

⇒ 2x - 1 = 9

⇒ 2x = 10

⇒ x = 5

Therefore, AB = 2x - 1 = 9 cm.

BC = 2x + 2 = 12 cm.

CA = 3x = 15 cm.

DE = 18 cm.

EF = 3x + 9 = 24 cm.

And, FD = 6x = 30 cm. (Answer)

Answer 2

We have Δ ABC and Δ DEF are similar.

Hence, \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}

DE

AB

=

EF

BC

=

FD

CA

So, \frac{2x - 1}{18} = \frac{3x}{6x}

18

2x−1

=

6x

3x

⇒ 2x - 1 = 9

⇒ 2x = 10

⇒ x = 5

Therefore, AB = 2x - 1 = 9 cm.

BC = 2x + 2 = 12 cm.

CA = 3x = 15 cm.

DE = 18 cm.

EF = 3x + 9 = 24 cm.

And, FD = 6x = 30 cm.