The length of the rectangle is greater than the breadth by 3cm. If the lengths increased by 9cm and the breadth is reduced by 5cm , the area remains the same. Find the dimensions of the rectangle
Answers
Step-by-step explanation:
let the breadth x
, , , , , length x+3
atq,
(x+3+9)(x-9) = area
as area of rectangle = l×b
(x+12)(x-9)= (x+3)x
after solving
x^2-9x+12x-108=x^2+3x
x^2+3x-108-x^2-3x=0
108cm^2 area
Answer:
Let the breadth of rectangle be x cm.
Then the length of rectangle will be
(x + 3) cm.
We know that , area of rectangle is given by;
Area = length•breadth
Thus,
Initial area = x(x+3) cm^2
Now;
New length after increasing it by 9 cm
= (x+3+9) cm
= (x + 12) cm
Also;
New breadth after reduced it by 5cm
= (x-5) cm
Thus,
Final area = (x-5)(x+12) cm^2
According to the question;
=> Initial area = Final area
=> x(x+3) = (x-5)(x+12)
=> x^2 + 3x = x^2 + 12x - 5x - 60
=> 12x - 5x - 3x = 60
=> 4x = 60
=> x = 60/4
=> x = 15
Thus,
Breadth of the rectangle = x cm
= 15 cm
Length of the rectangle = (x+3) cm
= (15+3) cm
= 18 cm
Hence, the length and the breadth of the rectangle are 18 cm and 15 cm respectively.