Question

perimeter of rectangular plot is 36 meters the length is increased by 6meters and breadth is decreased by 3 meters the area of the plot remains the same what is the length of the plot ​

Answer 1

Given:

Perimeter of a rectangular plot = 36 m.

Find:

length of the plot

Solution:

Let the length of the plot be x and it's breadth be y.

We know that,

Perimeter of a rectangle = 2(length + breadth)

⟹ 2(x + y) = 36

⟹ x + y = 36/2

⟹ x = 18 - y -- equation (1)

Also,

If length is increased by 6 m & breadth is decreased by 3 m , the area remains same.

Area of a rectangle = length * breadth

So,

(x + 6) * (y - 3) = xy

⟹ x(y - 3) + 6(y - 3) = xy

⟹ xy - 3x + 6y - 18 = xy

Substitute the value of x from equation (1).

⟹ - 3(18 - y) + 6y = 18

⟹ - 54 + 3y + 6y = 18

⟹ 9y = 18 + 54

⟹ y = 72/9

⟹ y = 8 m

Substitute the value of y in equation (1).

⟹ x = 18 - 8

⟹ x = 10 m

Hence,

Length (x) = 10 m

Breadth (y) = 8 m.

∴ The length of the plot is 10 m.

I hope it will help you.

Regards.