Question

The length of a rectangle is 5 cm greater than its width and its area is 150 cm2. The perimeter of the rectangle is

Answer 1

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Answer 2

Step-by-step explanation:

$let \: the \: lenghth \: of \: rectangle \: x \: cm \: \\ width = 5 + x \: \: (given) \\ area \: of \: rectangle \: = length \times width \\ 150 = x \times (5 + x) \\ 150= 5x + {x}^{2} \\ {x}^{2} + 5x - 150 = 0 \\ {x }^{2} + 15x - 10x - 150 = 0 \\ x(x + 15) - 10(x + 15) = 0 \\ (x + 15)(x - 10) = 0 \\ x + 15 = 0 \: \: or \: \: x - 10 = 0 \\ x = - 15 \: \: x = 10 \\ length \: is \: also \: possitive \: \\ x = 10 \\ length \: = 10 \\ width = 5+ x = 5 + 10 = 15 \\ perameter \: of \: rectangle \: = 2(length + width) = 2(10 + 15) \\ = 2(25) = 50$