Question

The length of a rectangle is 15 cm greater than its breath. Its perimeter is 150cm. Find the dimension of the rectangle​

Answer 1

Answer :

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• Dimensions of a rectangle are 30 cm and 45 cm.

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Explanation :

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Given :

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• Length of a rectangle is 15 cm greater than its breadth.

• It's perimeter is 150 cm.

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To Find :

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• Dimensions of rectangle?

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Solution :

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• Here, we are given that length of a rectangle is 15 cm greater than its breadth. So, Let's say that breadth be n cm. So, length is (n + 15) cm.

• Using well known formula, i.e, formula of perimeter of rectangle ::

• $\underline{\boxed{\bf{\red{Perimeter_{(rectangle)} = 2(\ell + b)}}}}$

• Where, $\bf{\ell}$ is length of a rectangle and b is breadth of a rectangle.

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$\clubsuit$ Putting all values in formula :

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➥ㅤ 2[n + (n + 15)] = 150

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➥ㅤ 2(n + n + 15) = 150

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➥ㅤ 2(2n + 15) = 150

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➥ㅤ 4n + 30 = 150

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➥ㅤ 4n = 150 – 30

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➥ㅤ 4n = 120

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➥ㅤ n = $\sf{\cancel{\dfrac{120}{4}}}$

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After cancelling 120 with 4, we get :

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➥ ㅤ$\underline{\boxed{\bf{\purple{n = 30}}}}\:\bigstar$

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Hence,

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• Breadth = n = 30 cm

• Length = n + 15 = 30 + 15 = 45 cm

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• Therefore, dimensions of a rectangle are 30 cm and 45 cm.

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$\clubsuit$ Know More :

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• Perimeter of square = 4 × side

• Perimeter of circle = 2πr

• Perimeter of equilateral ∆ = 3 × side

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Answer 2

Given :

• The length of a rectangle is 15 cm greater than its breadth.
• Perimeter of Rectangle is 150 cm.

To Find :

• Dimensions of the Rectangle .

Solution :

$\longmapsto\tt{Let\:Breadth\:be=x}$

As Given that length of a rectangle is 15 cm greater than its breadth . So ,

$\longmapsto\tt{Length=x+15}$

Using Formula :

$\longmapsto\tt\boxed{Perimeter\:of\:Rectangle=2(l+b)}$

Putting Values :

$\longmapsto\tt{150=2(x+15+x)}$

$\longmapsto\tt{150=2(2x+15)}$

$\longmapsto\tt{\cancel\dfrac{150}{2}=2x+15}$

$\longmapsto\tt{75-15=2x}$

$\longmapsto\tt{60=2x}$

$\longmapsto\tt{x=\cancel\dfrac{60}{2}}$

$\longmapsto\tt\bf{x=30}$

Value of x is 30 .

Therefore :

$\longmapsto\tt{Length\:of\:Rectangle=30+15}$

$\longmapsto\tt\bf{45\:cm}$

$\longmapsto\tt{Breadth\:of\:Rectangle=x}$

$\longmapsto\tt\bf{30\:cm}$