Question

17. The length and breadth of a rectangular park are in the ratio 5.2. A wide path of 25 m that
around the park has an area 425 sq m. Find the dimensions of the park.​

Answer 1

❅Correct Question:-

• The length and breadth of a rectangular park are in the ratio 5:2. A wide path of 2.5 m that around the park has an area 425 sq m. Find the dimensions of the park.

✽Given:-

• Ratio of length and breadth is 5:2
• Widht of the path is 2.5 m

❉To find:-

• Dimensions of the park

❊Solution:-

• Let the length be 5a and breadth 2a

↦Perimeter of rectangle =5a×2a=10a²

• Width of the path=2.5a

↠Outer length PQ=5a+2.5+2.5=5a+5

↠Outer length QR=2a+2.5+2.5=2a+5

$\sf \: Area \: of \: PQRS = (5a + 5)(2a + 5)$

$\sf \: = 10 {a}^{2} + 35a + 25$

$\sf \: Area \: of \: path = [(10 {a}^{2} + 35a + 25) - 10 {a}^{2} ]$

➠425=35a+25

➠35a=425-25

➠35a= 420

$\bf \: ➠a = \frac{420}{35} = 12$

$\bf \: Therefore \: length \: of \: the \: park =5a = 5 \times 12 = 60 \: m$

$\bf \: Therefore \: breadth \: of \: the \: park =2a = 2 \times 12= 24 \: m$

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$\large{ \underbrace{ \underline{ \color{maroon}{{ \bf \:learn \: more \: formula \: related \: to \: perimeter}}}}}$

➥Perimeter of rectangle =2×(length +breadth)

➥ Perimeter of square =4×side

➥Perimeter of triangle = sum of all sides

➥Circumference of circle =2πr

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• Refer to the attachment for the diagram :)