Question

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?
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Answer 1

Step-by-step explanation:

length of the rectangle = 40cm

breadth = 22cm

therefore the perimeter = 2(l+b)

=2(40+22)

=2 × 62

=124cm

area = l × b

=40×22

=880cm²

perimeter of the wire will be constant

therefore,

perimeter of the square

=4a = 124cm

=>a=124/4

=>a=31

therefore each side of the square is 31 cm

area = a²= 31²=961 cm²

therefore square encloses more area

Answer 2

Answer:

Step-by-step explanation:

Given :-

Length of the rectangle = 40 cm

 Breadth of the rectangle = 22 cm

To Find :-

Measure of Side.

Shape encloses more area.

Formula to be used :-

Perimeter of rectangle = 2 (L + B)

Perimeter of square  = 4 × Side

Area of rectangle = Length × Breadth

Area of square = (a)²

Solution :-

Let length of square is s.

As per the Question,

Perimeter of rectangle = Perimeter of square

⇒ 2×(Length + Breadth) = 4 × s

⇒   2 (40 + 22) = 4 × s

 ⇒ 2 × 62 = 4 × s

⇒  124 = 4 × s

 ⇒ s = 124/4

⇒ s = 31 cm

Area of rectangle = Length × Breadth

Area of rectangle =   40 × 22

Area of rectangle  = 880 cm²

Area of square = (a)²

Area of square  = 31 × 31

Area of square   = 961 cm²

Hence, the measure of each side is 31 cm.

Hence, square shaped wire encloses more area.