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# 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.

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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,

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1. 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

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