Question

The length of a rectangle is less than twice its breadth by 1 cm. If the length is reduced b
y 5cm and the breadth increased by 5cm, then its area increases by 35sq. Cm. Find the length
and breadth of the rectangle.

Answer 1

Answer: length =25 m and breath=13 m

Step-by-step explanation: let length =x and breath =y

from que, x=2y-1

(x-5) (y+5)=x×y  +35

xy + 5x - 5y -25= xy +35

5x-5y =35+25

5(x-y)=60

x-y=12

by putting the value of x,

2y-1 -y=12

y-1=12

y=13 and x=25

Answer 2

Answer:

Length of the rectangle is 25 cm. and breadth is 13 cm.

Step-by-step explanation:

Let breadth of a rectangle = x cm.

∴ Length = (2x - 1) cm.

Area of rectangle = length × breadth

                             = (2x-1) × x

                             = 2$x^{2}$ - x sq. cm.

If the length is decreased by 5 cm ., then new length = 2x- 1 -5= (2x- 6) cm.

If breadth is increased by 5 cm , then new breadth= x +5 cm.

New area = (2x-6 )× (x+5)

                 = x(2x - 6) + 5 (2x - 6)

                = $2x^{2}$ -6x +10x-30 = $2x^{2}$ +4x - 30

According to the given problem,

$2x^{2}$ +4x - 30 = 2$x^{2}$ - x +35

$2x^{2}$ - $2x^{2}$  +4x +x = 35 +30

                    5x= 65

                      x= 65/5 = 13

Breadth of the rectangle = 13 cm

Length of the rectangle = 2× 13 -1 =26 -1 =25 cm