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
A rectangle of area 105 cm² has its length equal to x cm.
Write down its breadth in terms of x. Given that the perimeter is 44 cm,
write down an equation in x and solve it to determine the dimensions of the rectangle.
Question no. 13, ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,
Solution:
Given:
Perimeter of rectangle = 44cm
Length + breadth = 44/2 = 22cm
Let us consider length be ‘x’
Breadth be ’22 – x’
So according to the question,
x(22 – x) = 105
22x – x2 – 105 = 0
x2 – 22x + 105 = 0
let us factorize,
x2 – 15x – 7x + 105 = 0
x(x – 15) – 7(x – 15) = 0
(x – 15) (x – 7) = 0
So,
(x – 15) = 0 or (x – 7) = 0
x = 15 or x = 7
Since length > breadth, x = 7 is not admissible.
∴ Length = 15cm
Breadth = 22 – x = 22 – 15 = 7cm