Question

4. Half the perimeter of a rectangular garden, whose
length is 4 m more than its width, is 36 m. Find
the dimensioni of the garden​

Answer 1

GivEn:

The denomitor of a fraction is 3 more than the numerator.

If 5 is added to both parts, the resulting fraction is equivalent to 4/5.

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To find:

Find the fraction?

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Solution:

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☯ Let the numerator be x then the denominator will be (x + 3).

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$\qquad\quad\boxed{\underline{\underline{\purple{\bigstar \: \bf\: According\:to\: Question\:\bigstar}}}}$

If 5 is added to both parts, the resulting fraction is equivalent to 4/5.

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$:\implies\sf \dfrac{(x + 5)}{(x + 8)} = \dfrac{4}{5}$

$:\implies\sf 5(x + 5) = 4(x + 8)$

$:\implies\sf 5x + 25 = 4x + 32$

$:\implies\sf 5x - 4x = 32 - 25$

$:\implies{\boxed{\sf{\pink{x = 7}}}}\;\bigstar$

Therefore,

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Numerator of fraction, x = 7

Denominator of fraction, (x + 3) = 10

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$\therefore$ Hence, The required fraction is 7/10.

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$\qquad\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\: Verification\:\bigstar}}}}$

According to 1st condition:

The denomitor of a fraction is 3 more than the numerator.

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→ 10 = 7 + 3

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According to 2nd condition:

if 5 is added to both parts, the resulting fraction is equivalent to 4/5.

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Adding 5 to both Numerator and Denominator,

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Numerator = (7 + 5) = 12

Denominator = (10 + 5) = 15

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→ 12/15 = 4/5

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Hence, Proved!

Answer 2

Answer:

20 meters

Step-by-step explanation:

 Let the width of the garden = x meter

Then length = ( x+4 )meter

Half perimeter = 36m

So perimeter of garden = (2×36)

                                        = 72 meters

According to the question

⇒ 2( l+b ) = 72

⇒ 2( x+x+4 ) = 72

⇒2x +2x +4 =74  x=16 meters

⇒ 4x = 64

x = 16 meters

Hence, the width of the garden = 16 meters

The length of the garden = ( 16+4 )

                                           = 20 meters

        I Hope this answer will help you.........