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.

336 cm²

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