Question

A rectangle of area 144cm.square has its length equal to x cm. Write down its breadth in terms of x. Given that its perimeter is 52cm, write down an equation in x and solve it to determine the dimensions of rectangle.
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Answer 1

Answer:-

Dimensions of the rectangle are 18cm [length] and 8cm [breadth] .

Explanation:-

We have :-

→ Area of the rectangle = 144 cm²

→ Length = x cm

→ Perimeter = 52 cm

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Let the assume that the breadth of the rectangle is 'b' cm.

Area of a rectangle = Length × Breadth

⇒ x × b = 144

⇒ b = 144/x

Hence, breadth in terms of 'x' is 144/x .

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Now :-

Perimeter of a rectangle :-

= 2( Length + Breadth )

⇒ 2( x + 144/x ) = 52

⇒ 2x + 288/x = 52

⇒ 2x² + 288 = 52x

⇒ 2x² - 52x + 288 = 0

⇒ 2(x² - 26x + 144) = 0

⇒ 2(x² - 8x - 18x + 144) = 0

⇒2[x(x - 8) - 18(x - 8)] = 0

⇒ 2(x - 18)(x - 8) = 0

⇒ x = 18 ; x = 8

Answer 2

Answer:

Given :-

Area of Rectangle = 144 cm²

Perimeter = 52 cm

To Find :-

Dimensions

Solution :-

Let

Breadth = b

We know that

$\mid \pmb{Area = l \times b} \mid$

$\mid \pmb{Perimeter = 2(l + b)} \mid$

144 = x × b

b = 144/x(1)

Perimeter = 2(l + b)

• Putting b as given in equation 1

52 = 2(x + 144/x)

52/2 = x + 144/x

26 = x + 144/x

26 × x = x + 144

26x = x² + 144

x² - 26x - 144 = 0

x² - (18x + 8x) - 144 = 0

x² - 18x - 8x - 144 = 0

x(x - 18) - 8(x - 18) = 0

(x - 18),(x - 8)

x = 18

Or,

x = 8

But length is always greater than breadth.

So,

Length = 18 cm

Finding breadth using equation 1

Breadth = 144/18

Breadth = 8 cm