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goblinko [34]
2 years ago
12

The length of a rectangular poster is 9 more inches than two times its width. The area of the poster is 161 square inches. Solve

for the dimensions (length and width) of the poster.
Mathematics
2 answers:
irinina [24]2 years ago
8 0

Answer:

<u>Width = 7 inches</u>

<u>Length = 23 inches</u>

Step-by-step explanation:

Let :

  • length = 2x + 9
  • width = x

Equating to area :

  • (2x + 9)(x) = 161
  • 2x² + 9x = 161
  • 2x² + 9x - 161 = 0
  • 2x² - 14x + 23x - 161 = 0
  • 2x(x - 7) + 23(x - 7) = 0
  • x - 7 = 0
  • x = 7

Dimensions are :

  • <u>Width = 7 inches</u>
  • Length = 2(7) + 9
  • <u>Length = 23 inches</u>
BaLLatris [955]2 years ago
7 0

Answer:

Length: 23 inches

Width: 7 inches

Explanation:

  • Width: w
  • Length: 2w + 9
<h3>Area of rectangle: Length × Width</h3>
  • (2w + 9) × (w) = 161
  • 2w² + 9w - 161 = 0
  • 2w² + 23w - 14w -161 = 0
  • w(2w + 23) -7(2w +23) = 0
  • w = 7, -11.5

As <u>length measure cannot be negative</u>. Width is +7 inches

Length: 2w + 9 = 2(7) + 9 = 14 + 9 = 23

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