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Kay [80]
2 years ago
15

Find the dimensions of the rectangle

Mathematics
1 answer:
ser-zykov [4K]2 years ago
3 0

Answer:

  • length: 12 m
  • width: 4.5 m

Step-by-step explanation:

The given relation between length and width can be used with the area formula to write an equation for the dimensions of the rectangle.

<h3>Setup</h3>

Let w represent the width of the rectangle. The length is 3 more than twice that, so is (2w+3). The area is the product of length and width.

  A = LW

  54 = (2w +3)(w)

<h3>Solution</h3>

Rewriting this equation to standard form gives ...

  2w² +3w -54 = 0

  (2w -9)(w +6) = 0 . . . . factored

  w = 9/2, -6 . . . . . . . . . values that make the equation true

Only the positive width makes sense in a geometry problem, so we have ...

  w = 9/2

  length = 2w +3 = 12

The length of the rectangle is 12 meters; its width is 4.5 meters.

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