Question

(b) The length of a rectangle shaped park exceeds its breadth by 17 meters. If the
perimeter of the park is 178 meters. Find the dimensions of the park?​

Answer 1

$\sf\underline\orange{Given:-}$

We are given that length of the rectangular park is 17 more than its breadth. We are also given that the perimeter of the rectangular park is 178m.

$\tt{\implies Length_{(rectangular\:park)} = Breadth_{(rectangular\:park)}+17}$

$\tt{\implies Perimeter_{(rectangular\:park)} = 178}$

$\sf\underline\orange{To\:find:-}$

We need to find the length and breadth of the rectangular park.

$\tt{\implies Length_{(rectangular\:park)}}$

$\tt{\implies Breadth_{(rectangular\:park)}}$

$\sf\underline\orange{Formulae\:applied:-}$

The formulae that we are going to apply in this problem is the formulae to find the perimeter of rectangle.

$\tt{\implies Perimeter_{(rectangular\:park)} = 2(l+b)}$

$\sf\underline\orange{Assumptions:-}$

We are assuming:

$\tt{\implies Breadth_{(rectangular\:park)} = x}$

Therefore, the length of the rectangular field will be:

$\tt{\implies Length_{(rectangular\:park)} = Breadth_{(rectangular\:park)}+17}$

$\tt{\implies Length_{(rectangular\:park)} = x+17}$

$\sf\underline\orange{Solution:-}$

Let us apply the formula of perimeter of the rectangular park to find its dimensions.

$\tt{\implies Perimeter_{(rectangular\:park)} = 178}$

$\tt{\implies 2(l+b) = 178}$

$\tt{\implies 2(x+17+x) = 178}$

$\tt{\implies 2(2x+17) = 178}$

$\tt{\implies 2x+17 = \dfrac{178}{2}}$

$\tt{\implies 2x+17 = 89}$

$\tt{\implies 2x = 89-17}$

$\tt{\implies 2x = 72}$

$\tt{\implies x = \dfrac{72}{2}}$

$\tt{\implies x = 36}$

Hence, from this we can say that:

$\tt{\implies Breadth_{(rectangular\:park)} = 36m}$

$\tt{\implies Length_{(rectangular\:park)} = 36+17}$

$\tt{\implies Length_{(rectangular\:park)} = 53m}$

$\sf\underline\orange{Conclusion:-}$

$\tt{\implies Breadth_{(rectangular\:park)} = 36m}$

$\tt{\implies Length_{(rectangular\:park)} = 53m}$

Answer 2

Answer:

Let the breadth of the park be = x metres

Then the length of the park be = x±17 metres

perimeter of the park=2( length ±breadth)

=2(x±17±x) metres

=2(2x±17) metres

But it is given that the perimeter of the rectangle is 178 metres.

2(2x ±17) =178

4x±34=178

4x =178-34

4x=144

x=144/4=36

Therefore breadth of the park=36 metres

Length of the park=36±17=53 metres.

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