Question

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QUESTION:-
The length of a rectangle is 10 more than its breath. If its area is 500cm, find the length and the breadth.

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Answer 1

Given Information:

The length of a rectangle is 10 more than its breath. If its area is 500cm, find the length and the breadth.

Solution:

Let the breadth of a rectangle be x

Then, the length will be x + 10

Area of rectangle = Length × Breadth

$\sf\tt{\implies500 = (x + 10) \times x}$

$\sf\tt{\implies{500 = x^{2} + 10x}}$

$\sf\tt{\implies{ {x}^{2} + 10x = 500}}$

$\sf\tt{\implies{ {x}^{2} + 10x + {5}^{2} = 500 + {5}^{2}}}$

$\sf\tt{\implies{ {x}^{2} + 10x + 25 = 500 + 25}}$

$\sf\tt{\implies{ {x}^{2} + 10x + 25=525}}$

$\sf\tt{\implies{(x + 5)^{2} = 525}}$

$\sf\tt{\implies{ \sqrt{(x + 5)^{2}} = \sqrt{525} }}$

$\sf\tt{\implies{x + 5 = 5 \sqrt{21} }}$

$\sf\tt{\implies{x + 5 = - 5 \sqrt{21} }}$

$\sf\tt{\implies{x = 5 \sqrt{21} - 5}}$

$\sf\tt{\implies{x = - 5 \sqrt{21} - 5}}$

$\sf\tt{\implies{x = 17.91 = 18}}$

$\sf\tt{\implies{x = - 27.91 = - 28}}$

Since, breadth cannot be negative,

So,

Breadth = x = 18cm

Length = x + 10 = 18 + 10 = 28cm

Answer 2

Answer:

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