ΔABC ~ ΔDEF and the perimeters of these triangles are 32 cm and 12 cm, respectively. If DE = 6 cm, then what will be the length of AB?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 1)

Answer 1

Given:

ΔABC ~ ΔDEF and the perimeters of these triangles are 32 cm and 12 cm.

DE = 6 cm

Concept used:

1. If two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion

2. The perimeter of a triangle is the sum of all its sides.

Calculation:

F7 Savita Teaching 6-6-23 D4

According to the question,

(AB + BC + AC) = 32 ....(1)

(DE + EF + DF) = 12 ....(2)

Since ΔABC ~ ΔDEF,

\(\frac {AB}{DE} = \frac {BC}{EF} = \frac {AC}{DF} = K(let)\)

From 1,

(AB + BC + AC) = 32

⇒ K(DE + EF + DF) = 32

⇒ K × 12 = 32

⇒ K = 32/12

⇒ K = 8/3

Now, AB

⇒ 8/3 × DE

⇒ 8/3 × 6 = 16 cm

∴ The length of AB is 16 cm.