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Q.

Perimeter of a square and a rectangle is the same. If a side of the square is 15cm and one side of the rectangle is 18cm, then the area of the rectangle is ____.


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Detailed Solution

Perimeter of a square and a rectangle is the same. If a side of the square is 15cm and one side of the rectangle is 18cm, then the area of the rectangle is 216 sq.cm.
Given that the perimeter of a square and a rectangle is the same.
Side of the square = 15 cm and one side of the rectangle = 18 cm.
Then,
Perimeter of a square = Perimeter of a rectangle
⇒4 × side = 2 × (l + b)
⇒4 × 15 = 2 × (18 + b)
⇒60 = 2 × (18 + b)
⇒ (18 + b ) =  602
⇒18 + b = 30
⇒b = 30 − 18
⇒b = 12
∴ Breadth of the rectangle is 12 cm
Now, we can find the area of the rectangle
Area of a rectangle = l × b
= 18 × 12
= 216
Therefore, area of a rectangle is 216 sq.cm.
 
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Perimeter of a square and a rectangle is the same. If a side of the square is 15cm and one side of the rectangle is 18cm, then the area of the rectangle is ____.