Question

Someone asked this 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?
I did it this way:
Answer:
Length = 40 cm
Breadth = 22 cm
Area of rectangular wire = 40 x 22 = 880 cm2
Sides in a square = 4
= 880/4
= 220 cm
Area of square = side x side = 220 x 220 = 48400 cm2
Answer: The measure of each side is 220 cm and the square encloses more area.
I checked my answer, it was wrong. Please tell me my mistake

Answer 1

Answer:

Hello,

Over here we have to find the perimeter first, not the area.

So by perimeter, we can find that length of wire = perimeter of rectangle

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

= 124 cm

Hence the side of the square which can be formed with this same wire is -

124 / 4

= 31 cm

Now, area of rectangle = l × b

= 40 × 22

= 880 cm²

The area of square = side × side

= 31 × 31

= 961 cm²

Hence, the area of square is larger.

I hope this answer helps you.