Question

the length and the breadth of a rectangular Park are in the ratio 5:2,a 2.5 m wide path running all around the outside of the park has an area of 305 sq.m. find the dimension of the park.




."ANSWER IS = 40m by 16m."
."SHOW ME EXPLLENATION"​

Answer 1

Let the length and Breadth of the rectangular park be 5x and 2x respectively.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

$\star\;\boxed{\sf{Area_{\:(rectangle)} = Length \times Breadth}}$

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Therefore,

$:\implies\sf 5x \times 2x \\\\\\:\implies\sf 10x^2$

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$\underline{\boldsymbol{According\: to \:the\: Question :}}$

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• A 2.5 m wide path running all around the outside of the park has an area of 305 m².

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Therefore,

• Length which is including path,

$:\implies\sf (5x + 2.5m + 2.5m) \\\\\\:\implies\sf (5x + 5)m$

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Similarly,

• Breadth which is including path,

$:\implies\sf (2x + 2.5 m + 2.5 m)\\\\\\:\implies\sf (2x + 5)m$

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Now, Area of the rectangular park:

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$:\implies\sf (5x + 5)m \times (2x + 5)m\\\\\\:\implies\sf (10x^2 + 25x + 10x + 25) m^2\\\\\\:\implies\sf (10x^2 + 35x + 25)m^2\\\\\\:\implies\sf (\cancel{10x^2}\; + 35x + 25) - \cancel{10x^2}\\\\\\:\implies\sf 35x + 25 = 305\\\\\\:\implies\sf 35x = 305 - 25\\\\\\:\implies\sf 35x = 280 \\\\\\:\implies\sf x = \cancel\dfrac{280}{35}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 8}}}}}$

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Hence, dimensions of the park are:

• Length of the park, 2x = 2(8) = 16m

• Breadth of the park, 5x = 5(8) = 40m

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$\therefore{\underline{\sf{Hence, \; Length \; and \; Breadth \: of \; the \: park \; are \: \bf{16m\: and \; 40m }.}}}$

Answer 2

Answer:

Given that :-

the length and the breadth of a rectangular Park are in the ratio 5:2,a 2.5 m wide path running all around the outside of the park has an area of 305 sq.m

Need to Find :-

Dimensions of park

Solution :-

Let the length be 5x and breadth be 2x

Now,

Area = Length × Breadth

Area = 5x × 2x

Area = 10x²

Now,

When 2.5 m added both sides

New Length = (5x + 2.5 + 2.5) = (5x + 5) m

New Breadth = (2x + 2.5 + 2.5) = (2x + 5) m

Now,

Area of park = (5x + 5) × (2x + 5)

305 = (10x² + 25x + 10x + 25)

305 = (10x² + 35x + 25)

305 = 10x² + 35x + 25 - 10x²

305 = 35x + 25

305 - 25 = 35x

35x = 280

$\sf \: x = \dfrac{280}{35}$

x = 8

Length = 5(8) = 40 m

Breadth = 3(8) = 24 m