Correct Answer - Option 4 : 62.13%
Given:
ΔABC ∼ ΔDEF
The heights of ΔABC and ΔDEF are in the ratio of 8 ∶ 13.
Concepts used:
The ratio of area of similar triangles is equal to the square of the ratio of perimeter or heights or sides of corresponding triangles.
Calculation:
ΔABC ∼ ΔDEF
⇒ ar(ABC)/ar(DEF) = [Height of ΔABC/height of ΔDEF]2
⇒ ar(ABC)/ar(DEF) = (8/13)2
⇒ ar(ABC)/ar(DEF) = 64/169
Let the ar(ABC) be 64x and ar(DEF) be 169x.
⇒ Percentage by which ar(ABC) is less than ar(DEF) = [(ar(DEF) – ar(ABC))/ar(DEF)] × 100
⇒ [(169x – 64x)/169x] × 100
⇒ 62.13%
∴ Area of ΔABC is less than the area of ΔDEF by 62.13%.