Question

A wire is in the shape of a rectangle. Its length is 50 cm and breadth is 26
cm. if the same wire is rebent is the shape of a square, what will be the
measures of each side? Also, find which shape has more area?​

Answer 1

Answer :-

• The measures of each side is 38cm.
• Square shape has more area.

Given :-

• A wire is in the shape of a rectangle.
• Length of the rectangle = 50cm.
• Breadth of the rectangle = 26cm.
• If the same wire is rebent is the shape of a square.

To find :-

• What will be the measures of each side?
• Also, find which shape has more area?

Solution :-

According to the question,

We know that,

• Perimeter of a rectangle = Perimeter of a square.

➞ 4 × Side = 2(Length + Breadth)

➞ 4 × Side = 2(50 + 26)

➞ 4 × Side = 2(76)

➞ 4 × Side = 152

➞ Side = $\dfrac{ 152}{4}$

➞ Side = 38cm.

Hence, The measures of each side of the square is 38cm.

Now, Let's find the area of rectangle and square :-

Area of rectangle = l × B = 50 × 26 = 1300cm².

Area of square = Side × Side = 38 × 38 = 1444cm².

Therefore, Square shape has more area.

Answer 2

Given:-

• A wire is in the shape of a rectangle and it's length is = 50cm
• A wire is in the shape of a rectangle and it's breadth is = 26cm
• If the same wire is rebent in the shape of a square

To Find:-

• What will be the measures of each side = ?
• Also,find which shape has more area =?

Solution:-

According to the question,

We know that,

Perimeter of a rectangle = Perimeter of a square

$\sf \implies4 \times side = 2(length + breadth) \\ \\ \sf \implies4 \times side = 2(50 + 26) \\ \\ \sf \implies4 \times side = 2(76) \\ \\ \sf \implies4 \times side = 152 \\ \\ \sf \implies side = \frac{152}{4} \\ \\ \sf \implies \: side = 38cm$

Hence,The measure of each side of the square is 38cm.

Now,Let's find the area of rectangle and square:-

Area of rectangle = l×b = 50 ×26 = $\sf{{1300cm}^{2}}$

Area of square = Side × Side = 38 × 38 = $\sf{{1444cm}^{2}}$

Therefore, square shape has more area.