Question

A wire is in the shape of a rectangle. It's length is 36 cm and breadth is 32 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?​

Answer 1

Answer:

34 cm, 1156 $cm^2$

Step-by-step explanation:

Total length of the wire remains same. So, perimeter of the rectangle would be the total length of the wire.

Perimeter: 2(36 + 32) = 136 cm

In a square, all 4 sides are equal:

136 = 4a :  a = 34 cm

So, each side of square is 34 cm. Area of square = 34 x 34 = 1156 $cm^2$

Hope it helps!

Answer 2

Answer:

Since the shape of the wire is changed from a rectangle to a square, therefore

Perimeter of the square = perimeter of the rectangle

$4 \: \times side \: = 2(length \: + \: breadth) \\ \\ 4 \times side \: = 2(36 + 32)cm \\ side = 2 \times \frac{68}{4} cm \: = 34cm$

Area of the square = (side)² = (34 cm)² = 1156cm²

Area of the rectangle = Length × breadth

= 36cm × 32cm = 1152cm²

Since 1156cm² > 1152cm², therefore the square encloses morea area.

✅ hence, the side of the square is 34cm and it encloses more area.

⛄ hope it helps you