Question

7. A wire is in the shape of a rectangle. Its length is 40 cm and breadth 22 cm. If the same wire is given the shape of a square, what will be the measure of each side? Also find which shape-rectangle or square-encloses more area?
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Answer 1

Answer:

Length= 40cm

Breadth= 22cm

Perimeter of the rectangle= Length of the wire

=2(l+b)= 2(40cm + 22cm)

=2\times622×62cm = 124cm

Now, the wire is rebent into a square.

Perimeter= 124cm

4\times side=1244×side=124

Therefore side= \frac{124}{4}

4

124

cm= 31cm

So, the measure of each side= 31cm

Area of rectangular shape= l\times bl×b

=40cm\times22cm40cm×22cm

=880cm^2880cm

2

Area of a square shape= \left(Side\right)^2(Side)

2

=\left(31\right)^2=961cm^2(31)

2

=961cm

2

Since 961cm^2\ >\ 880cm^2961cm

2

> 880cm

2

Hence, the square encloses more area.

Answer 2

Answer:

here's a simple way

side of square=31cm

A(square)>A(rectangle)

Step-by-step explanation:

Perimeter of rect. = 2(l+b)

= 2(40+22)

=2*62=124cm

Perimeter of sq. = 4* side

124 = 4* side

124/4 = side

side = 31cm

Area of rect. =l*b=40*22=880

Area of sq. = side*side= 31*31= 961

Area of sq. > Area of rect.