Question

The sides of two squares are in the ratio 4 : 3 and the sum of their areas is 225 cm2. Find the perimeter of the smaller square (in cm).

• A. 44
• B. 30
• C. 36
• D. 48

Answer 1

Answer:

C. 36

Solution: Given: The sides of two squares [(S1) and (S2)] are in the ratio 4 : 3 The sum of their Areas is 225 cm2. Formula used: The Perimeter (P) of the smaller square = 4 (side) Area of a Square = (side)2 Calculations: According to the question, S1/S2 = 4/3 ⇒ S1 = 4(S2)/3, and Then Areas of the Square: (S1)2 + (S2)2 = 225 ⇒ (4S2/3)2 + (S2)2 = 225 ⇒ 16(S2)2/9 + (S2)2 = 225 ⇒ 25 (S2)2/9 = 225 ⇒ 25 (S2)2 = 2025 ⇒ (S2)2 = 2025/25 ⇒ (S2)2 = 81 = 9 cm ⇒ S1 = (4 × 9)/3 ⇒ S1 = 36/3 = 12 cm The perimeter of the smaller square: ⇒ P = 4 × 9 = 36 cm ∴ The perimeter of the smaller square will be 36 cm.