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.
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