The perimeter of a square is the same as the perimeter of a rectangle. The perimeter of the square is 40 m. If its breadth is two-thirds of its length, then the area (in m2) of the rectangle is:
Answer & explanation
Correct answer: option 2
We know that,
Perimeter of rectangle = 2 × (Length + Breadth)
Area of rectangle = Length × Breadth
We have,
Perimeter of square = 40 m
Breadth of rectangle = Two-third of its length
The perimeter of square = Perimeter of rectangle
Let the length rectangle = 3a
Breadth = \(\frac{2}{3}\) × 3a = 2a
Perimeter = 2 × (Length + Breadth) = 40 = 2 × (3a + 2a)
= 20 = 5a
= a = 4
Length = 3a = 12 m
Breadth = 2a = 8 m
Area = Length × Breadth
= Area = 12 × 8 = 96 m2