A wire is in the shape of a square of side 10 cm. If the wire is rebent into a rectangle of length 12 cm, find its breadth. Which encloses more area, the square or the rectangle and by how much?
Mensuration
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Question

A wire is in the shape of a square of side 10 cm. If the wire is rebent into a rectangle of length 12 cm, find its breadth. Which encloses more area, the square or the rectangle and by how much?

KnowledgeBoat · Accepted Answer

Given: Side of square = 10 cm Length of rectangle = 12 cm Length of wire = Perimeter of square = 4 × side = 4 × 10 = 40 cm Since the wire is rebent into a rectangle, Perimeter of rectangle = Length of wire = 40 cm Perimeter of rectangle = 2(length + breadth) ⇒ 40 = 2(12 + breadth) ⇒ = 12 + breadth ⇒ 20 = 12 + breadth ⇒ breadth = 20 - 12 ⇒ breadth = 8 cm Area of square = side × side = 10 × 10 = 100 sq. cm Area of rectangle = length × breadth = 12 × 8 = 96 sq. cm Since 100 sq. cm 96 sq. cm, the square encloses more area. Difference in areas = 100 - 96 = 4 sq. cm Hence, the breadth of the rectangle is 8 cm and the square encloses more area than the rectangle by 4 sq. cm.

Mathematics

A wire is in the shape of a square of side 10 cm. If the wire is rebent into a rectangle of length 12 cm, find its breadth. Which encloses more area, the square or the rectangle and by how much?

Mensuration

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