SarkariPYQ

SSC CHSL 2024 PYQ — Question 62

SSC CHSL - 01 July 2024 - Shift 1 • Quantitative Aptitude • Q62

Back to paper

Given that the perimeters of two similar triangles, ∆ABC and ∆DEF, are 24 cm and 9 cm, respectively, and DE = 3 cm, what is the ratio between the area of ∆ABC and that of ∆DEF?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 64 : 9.

Given:

Perimeter of ΔABC = 24 cm

Perimeter of ΔDEF = 9 cm

DE (a side of ΔDEF) = 3 cm

First, we find the ratio of the perimeters:

Ratio of perimeters= PerimeterofΔABCPerimeterofΔDEF\frac{Perimeter of ΔABC}{Perimeter of ΔDEF} = 249\frac{24}{9} = 83\frac{8}{3}

Since the triangles are similar, the ratio of their corresponding sides is the same as the ratio of their perimeters:

The ratio of corresponding sides = 83\frac{8}{3}

The ratio between the area of ∆ABC and that of ∆DEF =  (83)2(\frac{8}{3})^2 = 649\frac{64}{9}  (The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides)