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Quadratic Equations in One Variable | Quadratic Equations in One Variable Exercise 5.5

Question 13

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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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

\begin{array}{l} 22 x-x^{2}-105=0 \\ x^{2}-22 x+105=0 \end{array}

let us factorize,

\begin{array}{l} x^{2}-15 x-7 x+105=0 \\ x(x-15)-7(x-15)=0 \end{array}

(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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Question 13

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.

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

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

\begin{array}{l} 22 x-x^{2}-105=0 \\ x^{2}-22 x+105=0 \end{array}

let us factorize,

\begin{array}{l} x^{2}-15 x-7 x+105=0 \\ x(x-15)-7(x-15)=0 \end{array}

(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

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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