In rectangle ABCD AB: BC = 1: 4. Find the area of a square whose perimeter is equal

In rectangle ABCD AB: BC = 1: 4. Find the area of a square whose perimeter is equal to the perimeter of this rectangle if the area of the rectangle is 144 cm².

Let’s designate the side AB of the rectangle as X cm, then BC is equal to 4 * X cm.

The area of the rectangle is:

Savsd = AB * BC.

144 = X * 4 * X.

X2 = 144/4 = 36.

X = AB = 6 cm, then BC = 4 * 6 = 24 cm.

Find the perimeter of the rectangle.

Ravsd = 2 * (AB + BC) = 2 * 30 = 60 cm.

Find the side of a square whose perimeter is 60 cm.

60/4 = 15 cm.

Then the area of the square is equal to: Sq = 15 ^ 2 = 225 cm2.

Answer: The area of the square is 225 cm2.