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Mathematics

The width of a rectangular room is 47\dfrac{4}{7} of its length, x, and its perimeter is y. Write an equation connecting x and y. Find the length of the room when the perimeter is 4400 cm.

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Answer

Given:

Length = x

Width = 47\dfrac{4}{7} of the length = 47×x\dfrac{4}{7} \times x

Perimeter = yy

Perimeter of a rectangle = 2(l + b)

⇒2(x+47x)=y⇒2(7+47x)=y⇒2(117x)=y⇒227x=y⇒ 2\Big(x + \dfrac{4}{7}x\Big) = y\\[1em] ⇒ 2\Big(\dfrac{7 + 4}{7}x\Big) = y\\[1em] ⇒ 2\Big(\dfrac{11}{7}x\Big) = y\\[1em] ⇒ \dfrac{22}{7}x = y\\[1em]

The length when y = 4400 cm,

⇒227x=4400⇒x=4400×722⇒x=3080022⇒x=1400cm=14m⇒ \dfrac{22}{7}x = 4400\\[1em] ⇒ x = \dfrac{4400 \times 7}{22}\\[1em] ⇒ x = \dfrac{30800}{22}\\[1em] ⇒ x = 1400 cm = 14 m

Hence, the equation connecting x and y is y=227xy = \dfrac{22}{7}x and the length of the room is 14 m.

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