Question

the length of a rectangular farm is 60 m. width 20m. what is the perimeter of the new rectangular farm formed by increasing the length of the field by 50% and reducing the width by 50%?

Answer 1

➤ Given :-

Length of rectangle :- 60 metres

Breadth of rectangle :- 20 metres

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➤ To Find :-

The perimeter if length is increased by 50% and width is decreased by 50%.

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★ How to do :-

Here, we are given with the length and the breadth of a rectangle. We are said that the length is increased by 50% and the breadth is decreased by 50%. We are asked to find the new perimeter of this rectangle. So, first we should find the new length and breadth of this rectangle. The appropriate formulas required are given while solving the problems. After, finding the new length and breadth, we can use the formula for calculating the perimeter. So, let's solve!!

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➤ Solution :-

Value of increased length :-

${\tt \leadsto 50 \bf\% \tt \: \: of \: \: 60}$

Replace the percentage by fraction form and 'of' as multiplication sign.

${\tt \leadsto \dfrac{50}{100} \times 60}$

Write the given fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{50}{100} \times 60 = \dfrac{1}{2} \times 60}$

Now, multiply the remaining numbers.

${\tt \leadsto \dfrac{1 \times 60}{2} = \dfrac{60}{2}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{60}{2} = 30 \: \: metres}$

Now, find the new length by adding the given length and increased length.

New length :-

${\tt \leadsto 60 + 30}$

${\tt \leadsto 90 \: \: Metres}$

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Now, find the value of decreased breadth.

Value of decreased breadth :-

${\tt \leadsto 50 \bf\% \tt \: \: of \: \: 20}$

Replace the percentage by fraction form and 'of' as multiplication sign.

${\tt \leadsto \dfrac{50}{100} \times 20}$

Write the given fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{50}{100} \times 20 = \dfrac{1}{2} \times 20}$

Now, multiply the remaining numbers.

${\tt \leadsto \dfrac{1 \times 20}{2} = \dfrac{20}{2}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{20}{2} = 10 \: \: metres}$

Now, find the new breadth by adding the given length and increased breadth.

New braedth :-

${\tt \leadsto 20 - 10}$

${\tt \leadsto 10 \: \: Metres}$

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Now, let's calculate for the needed perimeter...

Perimeter of the rectangle :-

${\tt \leadsto \underline{\boxed{\tt 2 \: ( Length + Breadth)}}}$

Substitute the given values.

${\tt \leadsto 2 \: (90 + 10)}$

Add the values which are in the bracket.

${\tt \leadsto 2 \: (100) = 2 \times 100}$

Now, multiply the numbers to get the answer.

${\tt \leadsto \pink{\underline{\boxed{\tt 200 \: \: Metres}}}}$

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Hence solved !!

Answer 2

Given

Length=60 cm

Breadth=20 cm

Find

the new rectangular farm formed by increasing the length of the field by 50% and reducing the width by 50%

Solution

Length=original+50% × original

∴60+50% × 60

∴60+50/100×60

∴60+5×6

∴60+30

=90 m

Now,

New Breadth-original-50%×original

∴20-50%×20

∴20-50/100×20

∴20-5×2

∴20-10

=10 m

Now,

By using formula of perimeter of rectangle=2(l+b)

∴perimeter of rectangle=2(90+10)

∴perimeter of rectangle=2(100)

∴perimeter of rectangle=200 m

Correct Answer

200 m