Question

The areas of a square and a rectangle are equal. The length of the rectangle is greater than the
length of any side of the square by 5 cm. and breadth is less by 3 cm. The perimeter of the
rectangle is
a) 17 cm b) 26 cm c) 34 cm
d) 30 cm e) None of these

Answer 1

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Answer 2

Dear Student,

● Answer - (c)

Perimeter of rectangle = 34 cm

● Explanation -

# Given -

l = s + 5

b = s - 3

# Solution -

We have areas of a square and a rectangle are equal.

Area of square = Area of rectangle

s² = l × b

s² = (s+5) (s-3)

s² = s² + 2s - 15

2s = 15

s = 7.5 cm

Now, we have -

l = s + 5 = 7.5 + 5 = 12.5 cm

b = s - 3 = 7.5 - 3 = 4.5 cm

Perimeter of rectangle is -

Perimeter of rectangle = 2 (l + b)

Perimeter of rectangle = 2 (12.5 + 4.5)

Perimeter of rectangle = 2 × 17

Perimeter of rectangle = 34 cm

Hence, perimeter of the rectangle is 34 cm.