Question

1. If the area of the rectangle is 105 cm ^ 2 Its length is (4x - 5) cm and breadth is (2x - 5) cm, find the perimeter?​

Answer 1

Answer:

If the area of the rectangle is 105 sq. cm  Its length is (4x - 5) cm and breadth is (2x - 5) cm, then the perimeter is 46 cm.

Step-by-step explanation:

Given:

Length = 4x - 5

Breadth = 2x - 5

The area of the rectangle is 105  sq. cm.

Find the perimeter of a rectangle.

Step 1: find length and breadth by using the area of the rectangle.

Area of rectangle = length × breadth

(4x - 5)(2x - 5) = 105

$8x^2 - 20x - 10x + 25 = 105\\8x^2 - 30x + 25 - 105 =0\\8x^2 - 30x - 80 = 0\\4x^2 - 15x - 40 = 0$

After solving we get x = 5.5 and x= -1.8

So, -1.8 is rejected

So, x = 5.5

So, length = [4(5.5) - 5 ]= 22 - 5 = 17 cm

And height = [2(5.5) - 5 ] = 11 - 5 = 6 cm

Step 2: Find the perimeter of the rectangle by using a formula.

Perimeter of rectangle = 2 (length + breadth)

= 2(17 + 6)

= 2(23)

= 46 cm

Hence the perimeter of rectangle is 46 cm.