Question

: The length of a rectangle shaped park exceeds its breadth by 17 meters. If th
perimeter of the park is 178 meters find the dimensions of the park?​

Answer 1

Given:-

• Perimeter of rectangular park is 178 m.

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To find:-

• Dimensions of park.

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Solution:-

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Let the breadth of rectangular park be x

And Let , Length of rectangular park will be x + 17

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We know that,

☘ Perimeter of rectangle = 2(l + b)

In which l is length of rectangle and b is breadth of rectangle.

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So, Put the values

⇒178 = 2(x + x + 17)

⇒178 = 2x + 2x + 34

⇒178 - 34 = 4x

⇒144 = 4x

⇒144/4 = x

⇒36 = x

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Verification:-

⇒178 = 2(x + x + 17)

• Put x = 36

⇒178 = 2(36 + 36 + 17)

⇒178 = 72 + 72 + 34

⇒178 = 178

Hence, verified.

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Thus, Dimensions of rectangular park are :-

✤ Length of park = 53 m

= x + 17

= 36 + 17

= 53 m

✤ Breadth of park = x = 36 m

Answer 2

Answer:

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Let the breadth of the park be = x meters

Then the length of the park = x+17 meters

Perimeter of the park = 2 (length + breadth)

= 2 (x + 17 + x) meters

= 2 (2x + 17) meters

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

$2(2x + 17) = 178 \\ 4x + 34 = 178 \\ 4x = 178 - 34 \\ 4x = 144 \\ x = \frac{144}{4} = 36$

Therefore breadth of the park = 36 meters

Length of the park = 36+17 = 53 meters.