Question

A rectangular has 240 cm perimeter,now increase its length 10% and decrease width 20% then perimeter remain same.So,find the length and width

Answer 1

1. 130

Step-by-step explanation:

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Answer 2

Answer:

Length = 80 cm

Width = 40 cm

Step-by-step explanation:

Let the length and width of the rectangle be x and y cm respectively. Hence, according to the first condition:

2(x + y) = 240

x + y = 120

y = 120 - x.......(1)

Next, when length is increased by 10% and width is decreased by 20%, then:

$New \: length = x \: + 10 \% \: of \: x \\ = x + \frac{10}{100} x = x + 0.1x \\ = 1.1x \\ New \: width = y \: - 20 \% \: of \: y \\ = y - \frac{20}{100} y = y - 0.2y \\ = 0.8y \\ \therefore \: new \: perimeter \: \\ 2(1.1x + 0.8y) = 240 \\ 1.1x + 0.8y = 120 \\ 11x + 8y = 1200..(multiplying \: both \: sides \: by \: 10) \\ 11x + 8y = 1200...........(2) \\ from \: equations \: (1) \: and \: (2) \\ 11x +8 (120 - x) = 1200 \\ 11x + 960 - 8x = 1200 \\ 3x = 1200 - 960 \\ 3x = 240 \\ x = \frac{240}{3} \\ x = 80 \: cm \\ \therefore \: y = 120 - 80 \\ y = 40 \: cm \\ thus \: the \: length \: and \: width \: of \: the \\ \: rectangle \: are \: 80 \: cm \: and \: 40 \: cm \: \\ respectively.$