A rectangle with perimeter 50 cm has its sides in the ratio 1 : 4. What is the perimeter of a square whose area is the same as that of the rectangle?
Answer & explanation
Correct answer: option 3
We know that,
Perimeter of rectangle = 2(l + b)
Area of a rectangle = l × b
Area of a square = a2
Given,
Perimeter of square = 4a
Perimeter = 50 cm
Ratio of sides = 1 ∶ 4
Let sides of the rectangle a and 4a
= 2(a + 4a) = 50
= 5a = 25
= a = 5
So, area of the rectangle = 4a2 = 4 × 25 = 100
a2 = 100
a = 10
Perimeter = 4 × 10 = 40 cm