Question

A thin wire in the shape of a rectangle is
straightened and bent again in the shape of a
square. If the sum of the length and breadth of the
rectangle is 28 cm, find the area of the square.​

Answer 1

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A thin wire in the shape of a rectangle is straightened and bent again in the shape of a square. If the sum of the length and breadth of the rectangle is 28 cm, find the area of the square.

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⋆ Given:-

A thin wire in the shape of a rectangle is straightened and bent again in the shape of square.Sum of length and breadth of the rectangle = 28 cm

⋆To Find:-

Area of the square.

Assumption:-

Let the length of the wire be L

And breadth be B.

⋆ Solution:-

Sum of length and breadth of wire=28cm

= L+B=28cm

Now,

Perimeter of the rectangular wire=2(L+B)

= Perimeter=2×28

= Perimeter=56cm

As the same wire with same dimension was straightened to form a square the perimeter will remain the same.

Therefore,

Perimeter of rectangular wire = Perimeter of square wire.

56=4×Side

$⟹Side= \frac{56}{4}$

⟹Side=14cm

Now,

We know,

Area of Square = (Side)²

Therefore,

$\bf{Area\:of\:wire\:in\:the\:shape\:of\:square = (14)^2}$

$= \bf{Area = 196\:cm^2}$

Therefore the Area of the wire in the shape of square is 196 cm².

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⋆ Formulas Used:-

Perimeter of rectangle = 2(Length + Breadth) units

Perimeter of square = 4×(side) units

Area of square = (side)² sq.units

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Answer 2

${\huge{\underline{\underline{\sf{\blue{Question:-}}}}}}$

A thin wire in the shape of a rectangle is straightened and bent again in the shape of a square. If the sum of the length and breadth of the rectangle is 28 cm, find the area of the square.

${\huge{\underline{\underline{\sf{\blue{Answer:-}}}}}}$

⋆ Given:-

A thin wire in the shape of a rectangle is straightened and bent again in the shape of square.Sum of length and breadth of the rectangle = 28 cm

⋆To Find:-

• Area of the square.

Assumption:-

Let the length of the wire be L

And breadth be B.

⋆ Solution:-

Sum of length and breadth of wire=28cm

= L+B=28cm

Now,

Perimeter of the rectangular wire=2(L+B)

= Perimeter=2×28

= Perimeter=56cm

As the same wire with same dimension was straightened to form a square the perimeter will remain the same.

Therefore,

Perimeter of rectangular wire = Perimeter of square wire.

56=4×Side

$⟹Side= \frac{56}{4}$

⟹Side=14cm

Now,

We know,

Area of Square = (Side)²

Therefore,

$\bf{Area\:of\:wire\:in\:the\:shape\:of\:square = (14)^2}$

$= \bf{Area = 196\:cm^2}$

Therefore the Area of the wire in the shape of square is 196 cm².

______________________________________

⋆ Formulas Used:-

• Perimeter of rectangle = 2(Length + Breadth) units

• Perimeter of square = 4×(side) units

• Area of square = (side)² sq.units

______________________________________