Question

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The area of a square is 49 sq.cm. A rectangle has the same perimeter as the square. If the
length of the rectangle is 9.3 cm., what is it's breadth? Also find which had greater area?
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Answer 1

Answer:

area of square =49

side of square =7

perimeter of square =4×7=28

perimeter of rectangle =28

2l+2b=28

l+b=14

9.3+b=14

b=4.7

Area of rectangle l×b

4.7×9.3=43.71

square has greater area

Answer 2

Answer :

• Breadth of the rectangle = 4.7 cm
• Area of square is greater than area of rectangle

Given :

• Area of square = 49 cm²
• Perimeter of the rectangle = Perimeter of square
• Length of the rectangle = 9.3 cm

To find :

• Breadth of the rectangle
• Which area is greater, area of square or area of rectangle

Concept :

To find the length of the rectangle :-

• Firstly, we will calculate the side of the square.
• Then after getting the value of the side of the square we will find the perimeter.
• The Perimeter of square will be equal to the perimeter of rectangle. (As mentioned in the question.)
• By substituting the given values in the formula of Periemeter of rectangle we will get the value of the length of the rectangle.

➳ Formula to calculate perimeter of the square :-

• Perimeter of square = 4 × side

➳ Formula to calculate area of square :-

• Area of square = side²

➳ Formula to calculate perimeter of rectangle :-.

• Perimeter of rectangle = 2(l + b)

➳ Formula to calculate area of rectangle :-

• Area of rectangle = l × b

where,

• l = length
• b = breadth

Solution :

Side of square :-

★ Area of square = side²

Substituting the given values,

→ 49 = side²

→ Taking square root on both the sides

→ √49 = side

→ ± 7 = side

→ As we know that side of the square cannot be in negative. So, the negative sign will get rejected.

→ ± 7 Reject - ve = side

→ 7 = side

• Side of the square = 7 cm

Using formula,

Perimeter of square = 4 × side

Substituting the given values,

→ Perimeter of square = 4 × 7

→ Perimeter of square = 28

• Perimeter of square = 28 cm

Perimeter of square = Perimeter of rectangle

Therefore,

• Perimeter of rectangle = 28 cm

Using formula,

Perimeter of rectangle = 2(l + b)

Substituting the given values,

→ 28 = 2(9.3 + b)

→ Transposing 2 to the left hand side.

→ 28 ÷ 2 = 9.3 + b

→ 14 = 9.3 + b

→ Transposing 9.3 to the left hand side. It's sign will change from positive to negative.

→ 14 - 9.3 = b

→ 4.7 = b

Therefore,

• Breadth of the rectangle = 4.7 cm

Area of rectangle :-

Using formula,

Area of rectangle = l × b

Substituting the given values,

→ Area of rectangle = 9.3 × 4.7

→ Area of rectangle = 43.71

• Area of the rectangle = 43.71 cm²

Area of square = 49 cm²

Area of rectangle = 43.71 cm²

Area of square > Area of rectangle

Area of square is greater than area of rectangle.