Question

the length of rectangle is 1 metre greater than its breadth if the length is increased by 2 metre and the breadth is decreased by 6 the area decreases by 50 metre square what are the dimension of the rectangle​

Answer 1

Answer:

18 m, 17 m

Step-by-step explanation:

Let breadth of rectangle = x.

Then,

Length = x + 1 m.

Area = Length * breadth

        = x * (x + 1)

       = x^2 + x

Now,

Length is increased by 2 metre and the breadth is decreased by 6.

New Length = x + 1 + 2 = x + 3

New Breadth = x - 6

Area = Length * breadth

        = (x + 3) * (x - 6)

       = x^2 - 6x + 3x - 18

       = x^2 - 3x - 18

But,

Given area decreases by 50 m^2.

=> x^2 - 3x - 18 = x^2 + x - 50

=> x = 17

Thus,

Length = 18 m

Breadth = 17 m

Hope it helps!

Answer 2

EXPLANATION

Let the l breadth of the rectangle be x.

Length= (x+ 1)

Area of rectangle= (x)(x+1) sq metre

According to the question

Length becomes (x+1+2) m when it is increased by 2 metres.

Breadth becomes (x-6) m when decreased by 6 m

$length \times breadth = area \\ (x + 2 + 1)(x - 6) = (x)(x + 1) - 50 \\ {x}^{2} + 3x - 6x - 18 = {x}^{2} + x - 50 \\ 32 = 4x \\ x = 8$

(Here, in the second step, in RHS, 50 m is decreased as area is decreased according to the question)

HENCE, Breadth of the rectangle= x= 8 m

Length= x+ 1= 8+1= 9 m