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.
Answers
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!