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

Answer:-

Given:

Perimeter of a rectangular plot = 36 m.

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.

Answer 2

Given :- Perimeter of rectangular plot is 36 meters. the length is increased by 6 meters and breadth is decreased by 3 meters the area of the plot remains the same what is the length of the plot ?

Solution :-

Let us assume that, length of rectangular plot is x m and breadth of rectangular plot is y m.

we know that,

• Perimeter of rectangle = 2(length + breadth).
• Area of rectangle = Length * breadth .

given that, perimeter of rectangular plot is 36m..

So,

→ 2(length + breadth) = 36

→ 2(x + y) = 36

dividing both sides by 2,

→ x + y = 18

→ y = (18 - x) -------------------- Eqn.(1)

Now, we have given that, if length is increased by 6 m and breadth is decreased by 3m area of rectangular plot remains same.

So,

→ Area of rectangular plot before = xy .

and,

→ New area of rectangular plot = (x + 6)(y - 3)

A/q,

→ (x + 6)(y - 3) = xy

→ xy - 3x + 6y - 18 = xy

→ 6y - 3x = 18

putting value of Eqn.(1) ,

→ 6(18 - x) - 3x = 18

→ 108 - 6x - 3x = 18

→ 108 - 9x = 18

→ 9x = 108 - 18

→ 9x = 90

dividing both sides by 9,

→ x = 10 m (Ans.)

Hence, Length of rectangular plot is 10m.

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