Question

ΔABC and ΔDEF are similar to each other. If the ratio of the area of ΔABC and ΔDEF is 9 ∶ 25, and the length of side AC is 21 cm. Find the length of DF.
1. 25
2. 30
3. 35
4. 45

Answer 1

Correct Answer - Option 3 : 35

Given:

ΔABC ~ ΔDEF

ar(ΔABC) : ar(ΔDEF) = 9 ∶ 25

Length of side AC = 21 cm

Concept:

If ΔABC ~ ΔDEF

ar(ΔABC)/ar(ΔDEF) = (AB/DE)2 = (BC/EF)2 = (AC/DF)2

Calculation:         

Let length of DF be x cm

According to the question, we have

(Area of ΔABC)/(Area of ΔDEF) = (AC/DF)2

⇒ (9/25) = (21/x)2

Taking square root on both the sides, we get

⇒ √(9/25) = √(21/x)2

⇒ (3/5) = (21/x)

⇒ x = (21 × 5)/3

⇒ x = 35 

∴ The length of DF is 35 cm.