Find the perimeter of a rectangle whose breadth is 1.5 times its length. The square has the same perimeter of the rectangle which is 84cm. Find the length of each side of the square. Also find the difference between the ratio of the area of the rectangle and the square.
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Step-by-step explanation:
Perimeter of the rectangle = Perimeter of the square = 84 cm
Assumption 1: Let the length (l) of the rectangle be x cm.
So, breadth (b) = 1.5x cm
Perimeter = 2×(l + b)
=> 84 = 2(x + 1.5x)
=> 84/2 = 2.5x
=> 42/2.5 = x
=> 16.8 = x
So,
length = x cm = 16.8 cm
breadth = 1.5x cm = 1.5 × 16.8 cm = 25.2 cm
Assumption 2: Let the sides of the square be a cm each.
Perimeter = 4 × side
=> 84 = 4a
=> 21 = a
Side of the square = a cm = 21 cm
Area of the square = 21 × 21 cm² = 441 cm²
Area of the rectangle = 16.8 × 25.2 cm² = 423.36 cm²
Ratio of area of the rectangle to area of the square =
423.36 cm² : 441 cm²
= 24:25
Difference between area of the rectangle and area of the square = 441 - 423.36 cm²
= 17.64 cm²
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