Question

The length of a rectangle is (2x + 3) units and its breadth is
(2x
3) units. Find the area of the rectangle in terms of x
What will be the area of the rectangle if X 30 units?
RETETET​

Answer 1

Correct Question:

The length of a rectangle is (2x + 3) units and its breadth is (2x-3) units. Find the area of the rectangle in terms of x. What will be the area of the rectangle if x = 30 units?

Step-by-step explanation:

Given:

• Length of the rectangle = (2x+3) units
• Breadth of the rectangle = (2x-3) units

To find:

• Area of the rectangle in terms of x.
• Area of the rectangle if x= 30 units

Solution:

We know that,

★Area of rectangle= Length × Breadth ★

• [ Put values ]

Area of the rectangle = (2x+3)×(2x-3) units ²

→ Area of the rectangle = (2x)² - 3² units ²

→ Area of the rectangle = (4x²-9) units²

When x= 30 units,

• Length = (2×30+3) = 63 units
• Breadth = (2×30-3) = 57 units

Then,

Area of the rectangle = (63×57) units²

→ Area of the rectangle = 3591 units²

_________________

Answer 2

Correct Question :-

The length of a rectangle is (2x + 3) units and its breadth is (2x-3) units. Find the area of the rectangle in terms of x. What will be the area of the rectangle if x = 30 units ?

Given :-

• Length of the rectangle (l) = (2x + 3) units
• Breadth of the rectangle (b) = (2x - 3) units

To Find :-

• Area of the rectangle in terms of x = ?
• Area of the rectangle if x is 30 units = ?

Concept Used :-

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• (a + b) (a - b) = a² - b²
• Area of rectangle = Length × Breadth

Solution :-

Let's find the area of the rectangle.

❖ Area of rectangle = Length × Breadth

⇒ Area of rectangle = (2x + 3) × (2x - 3) unit²

⇒ Area of rectangle = (2x)² - (3)²  unit²   [Using (a + b) (a - b) = a² - b²]

⇒ Area of rectangle = (4x² - 9) unit²

∴ The area of rectangle in terms of x is (4x² - 9) unit².

Now we put the value of x as 30

◆ Area of rectangle = (4x² - 9) unit²

⇒ Area of rectangle = [{4 × (30)²} - 9] unit²

⇒ Area of rectangle = {(4 × 900) - 9} unit²

⇒ Area of rectangle = (3600 - 9) unit²

⇒ Area of rectangle = 3,591 unit²

∴ The area of rectangle when x is 30 units is 3591 unit².

Additional Information :-

• Perimeter of rectangle = 2(Length + Breadth)
• Area of rectangle = Length × Breadth
• Length of diagonal of rectangle = √Length² + Breadth²
• Perimeter of square = 4 × Length of a side of square
• Area of square = Side²
• Length of diagonal of square = Side√2
• Perimeter of triangle = Length of the sides of triangle
• Area of triangle = ½ × Base × Height