A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side? Also find which shape encloses more area?
Explain in detail.
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Answers
Length of the rectangle = 40 cm
Breadth of the rectangle = 22 cm
Since same length of wire is used to form a rectangle and square, we can say that,
perimeter of square = perimeter of rectangle
4 × Side = 2 (Length + Breadth)
4 × Side = 2 (40 + 22)
4 × Side = 2 × 62
4 × Side = 124
Side = 124/4
Side of square = 31 cm
Area of square = side × side
= 31 cm × 31 cm
= 961 cm2
Area of rectangle = Length × Breadth
= 40 cm × 22 cm
= 880 cm2
Hence, square shape encloses more area.
Step-by-step explanation:
Perimeter of the rectangle
= 2 × ( L+B )
= 2 × ( 40+22) = 124 cm
»» Perimeter of the square = 124 cm
»» 4 × Side = 124
»» Side = 124/4 cm = 31 cm
Hence, the measure of each side of the square is 31 cm.
i) Area of the rectangle
= L×B
= 40 × 22 cm² = 880 cm²
ii) Area of the square
= side × side
= 31 × 31 = 961 cm²
Hence, the square encloses more area.
hope it helps you.