This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5
This is an important ques
The perimeter of a rectangular plot is 180 m and its area is 1800 m².
Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x.
Use the values of length, breadth and the area to write an equation in x.
Solve the equation to calculate the length and breadth of the plot.
Question no. 16 , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,
Solution:
Given,
The perimeter of a rectangular field = 180 m
And area = 1800 m²
Let’s assume the length of the rectangular field as ‘x’ m
We know that,
Perimeter of rectangular field = 2 (length + breadth)
So, (length + breadth) = perimeter/ 2
x + breadth = 180/2
⇒ breadth = 90 – x
Now, the area of the area of the rectangular field is given as
Length × breadth = 1800
x × (90 – x) = 1800
90x – x2 = 1800
x2 – 90x + 1800 = 0
Upon factorization, we have
x2 – 60x – 30x + 1800 = 0
x(x – 60) – 30(x – 60) = 0
(x – 30) (x – 60) = 0
So,
x – 30 = 0 or x – 60 = 0
x = 30 or x = 60
As length is greater than its breadth,
Therefore, for the rectangular field
Length = 60 m and breadth = (90 – 60) = 30 m