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Question
The length of a rectangle is 3 m more than its width. If its area is 180 m2; the length of the rectangle is ______.
Options
12 m
9 m
15 m
10 m
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Solution
The length of a rectangle is 3 m more than its width. If its area is 180 m2; the length of the rectangle is 15 m.
Explanation:
Let the width of rectangle = x metre
∴ Length of rectangle = (x + 3) metre
Given area of rectangle = 180 m2
`\implies` x(x + 3) = 180
`\implies` x2 + 3x – 180 = 0
`\implies` x2 + 15x – 12x – 180 = 0
`\implies` x(x + 15) – 12(x + 15) = 0
`\implies` (x + 15)(x – 12) = 0
Either x + 15 = 0 or x – 12 = 0
`\implies` x = –15 or 12
But x > 0
∴ x = 12
Thus length of rectangle = x + 3
= (12 + 3) m
= 15 metre
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