Question

area of squre is 324 squre cm and length of rectangle is 13.5cm what is difference between the breadth of rectangle and the side of square
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Answer 1

Correct Question:

The area of a square is twice the area of rectangle. If the area of square is 324 square centimetres and the length of the rectangle is 13.5 cm. What is the difference between the breadth of the rectangle and the side of the square?

Answer:

• The difference between the breadth of the rectangle and the side of the square is 6 cm.

Step-by-step explanation:

Given that:

• The area of a square is twice the area of rectangle.
• The area of square is 324 square centimetres.
• The length of the rectangle is 13.5 cm.

To Find:

• What is the difference between the breadth of the rectangle and the side of the square?

Let us assume:

• Area of rectangle be x.

Finding the area of rectangle:

According to the question.

⇒ 2x = 324

⇒ x = 324/2

⇒ x = 162

∴ Area of rectangle = 162 cm²

Now finding the breadth of rectangle:

Formula: Area of rectangle = (Length × Breadth)

Substituting the values.

⟶ 162 cm² = 13.5 cm × Breadth

⟶ Breadth = (162 cm²)/(13.5 cm)

⟶ Breadth = 12 cm

∴ Breadth of rectangle = 12 cm

Finding the side of square:

Formula: Area of square = (side × side)

Substituting the values.

⟶ 324 cm = (side × side)

⟶ side × side = 18 cm × 18 cm

⟶ side = 18 cm

∴ Side of square = 18 cm

Finding the difference between the breadth of the rectangle and the side of the square:

Formula: Difference = Bigger value - Smaller value

⇒ Difference = 18 cm - 12 cm

⇒ Difference = 6 cm

∴ The difference between the breadth of the rectangle and the side of the square = 6 cm

Answer 2

Appropriate Question :

• The area of a square is twice the area of a rectangle . If the area of square is 324 cm² and the length of the rectangle is 13.5 cm . What is the difference between the Breadth of the rectangle and the side of the square .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Given : The area of a square is twice the area of a rectangle , the area of square is 324 cm² and the length of the rectangle is 13.5 cm .

Exigency to find : The difference between the Breadth of the rectangle and the side of the square .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider the Side of Square be x cm .

⠀⠀⠀⠀⠀Finding Side of a Square :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Area_{(Square)} \:: a^2 }\bigg\rgroup$

⠀⠀⠀⠀⠀Here a is the Side of Square & we have given with the area of Square is 324 cm² .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \longmapsto \sf 324 = x^2$

$\qquad \longmapsto \sf \sqrt {324} = x$

$\qquad \longmapsto \frak{\underline{\purple{ x = 18 cm }} }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Side \:of\:Square \:is\:\bf{18\: cm}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀Finding Area of a Rectangle :

❒ Let's consider Area of Rectangle be x .

Given That ,

• The area of a square is twice the area of a rectangle .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \: To \: Question \::}}$

$\qquad \longmapsto \sf 2x = 324$

$\qquad \longmapsto \sf x = \cancel {\dfrac{324}{2}}$

$\qquad \longmapsto \frak{\underline{\purple{ x = 162 cm^2 }} }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Area \:of\:Rectangle \:is\:\bf{162\: cm^2}}}}$

⠀⠀⠀⠀⠀Finding Breadth of a Rectangle :

❍Let's Consider Breadth of Rectangle be b cm .

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Area_{(Rectangle)} \:: l \times b }\bigg\rgroup$

⠀⠀⠀⠀⠀Here l is the Length of Rectangle & b is the Breadth of Rectangle and we know that Area of Rectangle is 162 cm^2 .

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \longmapsto \sf 162 = 13.5 \times b$

$\qquad \longmapsto \sf b = \cancel {\dfrac{162}{13.5}}$

$\qquad \longmapsto \frak{\underline{\purple{ b = 12 cm }} }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Breadth \:of\:Rectangle \:is\:\bf{12\: cm}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀⠀⠀Finding the difference between the Breadth of the rectangle and the side of the square :

• Breadth of Rectangle is 12 cm
• Side of Square is 18 cm .

As , We can see that ,

Here ,

• Side of Square is greater than Breadth of Rectangle.

Therefore,

$\qquad \dag\:\:\bigg\lgroup \sf{ Difference \::Side_{(Square)} - Breadth_{(Rectangle)} }\bigg\rgroup$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \longmapsto \sf Difference = 18- 12$

$\qquad \longmapsto \frak{\underline{\purple{ Difference = 6 cm }} }$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Difference \:between \:them \:is\:\bf{6\: cm}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀