Question

the length of a rectangle is 2 x + 3 units and the corresponding breadth is 2 x minus 3 units find the area of the rectangle in terms of X what will be the area of rectangle if x is equal to 30 units​

Answer 1

Answer:

Length , l = 2x +3 units

Breadth, b = 2x - 3 units

Area of rectangle= l×b

Area of rectangle = (2x+3)(2x-3)

[ using identity (a+b)(a-b)= a^2-b^2 ]

Area of rectangle= (2x)^2 - (3)^2

Area of rectangle =4x^2 - 9

So, area of rectangle in terms of x will be 4x^2 -9 square units.

When x =30 units

Then,

Area of rectangle= 4(30)^2 -9

Area of rectangle= 4×900 -9

Area of rectangle = 3591 sq. units

Answer 2

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