Question

The length of a rectangle is greater then the breadth by 18cm. if both length & breadth are increased by 6cm,the area increases by 168cm^2. Find the length and breadth of the rectangle.
ch-linear equation.​

Answer 1

Let the breadth of the rectangle be x.

Then the length of the rectangle will be greater than the breadth by 18cm = (x+18) cm.

We know that Area of the rectangle = l * b

= x * (x + 18)

= x^2 + 18x ------------- (1)

Given that breadth of the rectangle is increased by 6cm. = (x+6)cm.

Then the length of the rectangle = (x + 6 + 18)

= (x + 24).

Now the area of the rectangle = (x + 6)(x + 24)

= x^2 + 24x + 6x + 144

= x^2 + 30x + 144 ------------ (2)

On solving (1) and (2) with the increased area by 168cm^2.

x^2 + 18x + 168 = x^2 + 30x + 144

18x + 168 = 30x + 144

12x = 24

x = 2.

If the breadth is 2cm Then the length will be (2 + 18) = 20cm.

Therefore the length = 20cm and the breadth = 2cm.

Hope this helps!