Question:
A wire in the form of a square encloses an area of 144cm how much area is enclosed if the same wire is bent in the form of a rectangle of length of 16cm ?
A wire in the form of a square encloses an area of 144cm how much area is enclosed if the same wire is bent in the form of a rectangle of length of 16cm ?
Updated On: Aug 8, 2023
48 cm2
128 cm2
96 cm2
124 cm2
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The Correct Option is B
Solution and Explanation
When the same wire is twisted to create the shapes of a rectangle and a square, their perimeters will match.
Area of the rectangle = Length × Breadth
Area of the square = side2
The perimeter of the square = 4 × side
Perimeter of the rectangle = 2(length + breadth)
Area of the square = 144 cm2
⇒ side, (a) = √144 = 12 cm
Perimeter of the square = Perimeter of the rectangle = 4 × 12 = 48 cm
Now, Perimeter of the rectangle = 2(length + breadth)
⇒ 2(16 + breadth) = 48
⇒ breadth = 24 - 16 = 8 cm
So, Area of the rectangle = 16 × 8 = 128 cm2
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