Question

The Perimetre of a rectangular field is 130m. If its length is 5m more that its bradth, find the length & breadth of the field.


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Answer 1

Question:

The perimeter of a rectangular field is 130m. If it's length is 5m more than it's breadth, find the length and breadth of the rectangular field.

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Given In Question: The Perimeter of the rectangular field is 130m. & it's Length is 5m more than it's breadth.

Need to Calculate: The dimensions of the field?

❍ Let's say, that the Breadth of the field be x m. Then, it's Length be (x + 5) m respectively.

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To find the dimensions of the given rectangular field, we can use the Perimeter formula of rectangle. That is given By :

$\dashrightarrow\sf Perimeter_{\:(rectangle)} = 2\bigg\{Length + Breadth\bigg\}$

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On Substituting the given Values in the above formula, we get:

$\dashrightarrow\sf 130 = 2\Big\{(x + 5) + x\Big\}$

On transposing '2' to the LHS, we get:

$\dashrightarrow\sf \cancel\dfrac{130}{2} = 2x + 5$

$\dashrightarrow\sf 65 = 2x + 5$

On transposing '5' to the LHS, we get:

$\dashrightarrow\sf 65 - 5 = 2x$

$\dashrightarrow\sf 60 = 2x$

On dividing 2 by 60, we get:

$\dashrightarrow\sf x = \cancel\dfrac{60}{2}$

$\dashrightarrow{\pmb{\sf{x = 30\;m}}}$

We know that, value of x is '30'. Therefore, we'll substitute the value of x in given Length (30 + x) to find out the Length. Therefore —

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$\twoheadrightarrow\sf Length = 30 + 5$

$\twoheadrightarrow{\pmb{\sf{Length = 35\;m}}}$

Hence,

• Length of the field = 35m
• Breadth of the field = 30m

∴ Therefore, the Length and Breadth of the rectangular field are 35m and 30m respectively.

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M o r e⠀F o r m u l a e :

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$\sf Area\:of\:rectangle = \bf{Length \times Breadth}$

$\sf Diagonal\:of\:rectangle = \bf{\sqrt{(Length)^2 + (Breadth)^2}}$

$\sf Perimeter\:of\:square = \bf{4 \times side}$

$\sf Diagonal\:of\:square = \bf{ \sqrt{2} \times side}$