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Question
Perimeter of a square and a rectangle is same. If a side of the square is 15 cm and one side of the rectangle is 18 cm, find the area of the rectangle.
Solution
Let breadth of rectangle = b cm
Given, length of rectangle = 18 cm
And side of a square = 15 cm
∴ Perimeter of a square = 4 × Side = 4 × 15 = 60 cm
Given, Perimeter of rectangle = Perimeter of square
⇒ 2 × (Length + Breadth) = 60
⇒ 2(18 + b) = 60
⇒ `(2 xx (18 + b))/2 = 60/2` ......[Dividing both sides by 2]
⇒ 18 + b = 30
⇒ b = 30 – 18 ......[Transposing 18 to RHS]
⇒ b = 12
Now, Area of rectangle = Length × Breadth
= 18 × 12
= 216 sq cm
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