Question

the length and breadth of a rectangular park are in ratio 5:2.if its perimeter is 168 m.find its length and breadth​

Answer 1

Given, the length and breadth of a rectangular park are in the ratio 5:2.

Let the length and breadth of the rectangle be 5x,2x.

Then perimeter will be 2(5x+2x)=14x.

According to the problem,

14x=140

or, x=10.

Then length and breadth will be 50 cm and 20 cm.

Then area will be 50×20=1000 cm

2

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Answer 2

Given :

• Ratio of the length and breadth of the rectangular park = 5 : 2
• Perimeter of the rectangular park = 168 m

To find :

• Length and breadth of the park

Concept :

To find the length and breadth of the park, firstly we will assume the length and breadth as 5a and 2a. By substituting the values in the formula of perimeter of rectangle and after solving it, we will get the value of a. Substitute the value of a in the dimensions of the rectangular park which we've let, the resultant values will be our required answer.

Formula of perimeter of rectangle :-

• Perimeter of rectangle = 2(l + b)

where,

• l stands for the length of the rectangle

• b stands for the breadth of the rectangle

Solution :

Let,

• Length of rectanglular park = 5a
• Breadth of rectangular park = 2a

Using formula,

★ Perimeter of rectangular park = 2(l + b)

Substituting the given values, we get :-

➪ 168 = 2(5a + 2a)

➪ Adding the values present in the brackets.

➪ 168 = 2(7a)

➪ Transposing 2 to the left hand side.

➪ 168 ÷ 2 = 7a

➪ 84 = 7a

➪ Transposing 7 to the left hand side.

➪ 84 ÷ 7 = a

➪ 12 = a

The value of a = 12

Substituting the value of a in the dimensions of the rectangular park :-

→ Length of the rectangular park = 5a = 5 × 12 = 60 m

→ Breadth of the rectangular park = 2a = 2 × 12 = 24 m

Therefore,

• Length and breadth of the rectangular park are 60 m and 24 m respectively.

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VERIFICATION :

To verify the answer, find the perimeter of the rectangular park. If the perimeter will be equal to 168 m (as mentioned in the question) then the answer is right.

Perimeter of rectangular park = 2(l + b)

we have,

• l = 60 m
• b = 24 m

Substituting the values,

→ Perimeter of rectanglular park = 2(60 + 24)

→ Perimeter of rectanglular park = 2(84)

→ Perimeter of rectanglular park = 168

Perimeter of the rectangular park = 168 m

HENCE, VERIFIED.