The perimeter of a square is equal to the perimeter of a rectangle, and the latter has a width of 12 cm. The area of the square is 400 cm2. Find the area of the rectangle.
Answer & explanation
Correct answer: option 4
We already know that,
Area of a square = (side)2
Area of a rectangle = Length × Breadth
The perimeter of a square = 4a
Perimeter of a rectangle = 2(L + B)
We have,
The perimeter of a square = perimeter of a rectangle,
The rectangle has a width = 12 cm.
The area of the square is 400 cm2
So,
(side)2 = 400 cm2
= side = 20
So, perimeter = 20 × 4 = 80 cm
Now, 2(L + 12) = 80
= L + 12 = 40
= L = 28 cm
So, the area of the rectangle = 28 × 12 = 336 cm2