Question

the perimeter of a rectangle is 360m. if its length is decresed by 20 % and its breadth is increased by 25% we get the same perimeter . find the dimention of the rectangle

Answer 1

Step-by-step explanation:

answer is in the pic.

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Answer 2

Answer

☞ Length = 100 m

☞ Breadth = 80 m

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$\huge\sf\blue{Given}$

✭ Perimeter of a rectangle is 360 m

✭ If the perimeter is decreased by 20% & the breadth is increased by 25% the perimeter is the same

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$\huge\sf\gray{To \:Find}$

◈ The dimensions of the rectangle?

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$\huge\sf\purple{Steps}$

We know that perimeter of a rectangle is given by,

$\underline{\boxed{\sf Perimeter_{Rectangle} = 2(l+b)}} </p><p>$

Perimeter = 360 m

$➢ \sf2(l+b) = 360 \\ </p><p></p><p>➢ \sf l+b = \dfrac{360}{2}</p><p>$

$➢ \sf l+b = 180 \:\:\ -eq(1)$

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

When the length is decreased by 20%

$➝ ➝ \sf l-\dfrac{20l}{100}$

$➝ \sf\dfrac{100l-20l}{100} </p><p></p><p>$

$</p><p>➝ \sf\dfrac{80l}{100} </p><p>$

$➝ \sf\dfrac{8l}{10} </p><p>$

When the breadth is increased by 25%

$➝ \sf b+\dfrac{25b}{100}$

$➝ \sf b+\dfrac{1b}{4}$

$➝ \sf\dfrac{4b+1b}{4}$

$➝ \sf\dfrac{5b}{4} </p><p>$

So now given that their perimeter is 360

$➳ \sf2\bigg\lgroup \dfrac{8l}{10} + \dfrac{5b}{4}\bigg\rgroup = 36$

$➳ \sf2\bigg\lgroup\dfrac{16l+25b}{20}\bigg\rgroup = 36$

$➳ \sf16l+25b = 360\times 10$

$➳ \sf16l+25b = 3600 \:\:\ -eq(2)$

Multiplying eq(1) by 16 and subtracting it from eq(2)

$➠ \sf(16l+25b)-(16l+16b) = 3600</p><p>$

$➠ \sf16l+25b-16l-16b = 720$

$➠ \sf9b = 720 \\ </p><p></p><p>➠ \sf b = \dfrac{720}{9}$

$➠ \sf\pink{Breadth = 80 \ m}$

Substituting the value of b in eq(1)

$»» \sf l+b =180 \\ </p><p></p><p></p><p>»» \sf l = 180-80$

$»» \sf \orange{Length = 100 \ m}$