Question

a wire which is bent in the shape of a square of area 49 CM square is bent to form a rectangle of breath 4 cm find the area of a rectangle formed on building the wire also find which shape occupies more area and by how much​

Answer 1

Answer :

• The area of the square occupies more than the rectangle by 9 cm².

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Given :

• Area of Square = 49 cm
• Breadth of Rectangle = 4 cm

To find :

• the area of the rectangle
• which shape occupies more area and by how much​.

Solution :

⇒ Let's find the Side of the square.

→ Area of Square = s²

49 cm² = s²

s = √49

= 7 cm

⇒ Now, the perimeter of the square and rectangle are the same.

→ Perimeter of square = 4 × s

= 4 × 7

= 28 cm

→ Perimeter of Rectangle = 28cm

Perimeter = 2(l + b)

28 = 2(l + 4)

28 = 2l + 8

28 - 8 = 2l

20 = 2l

l = 10 cm

⇒ Now, let's find the Area of each.

Area of Square = 49 cm²

→ Area of Rectangle = length × breadth

= 10 × 4

= 40 cm²

Since,

• 49 cm² ≥ 40 cm²
• Area of Square ≥ Area of Rectangle

Difference = 49 - 40

= 9 cm²

• Therefore, the area of the square has more area by 9 cm².