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borishaifa [10]
3 years ago
15

The length of a rectangle is 9 centimeters more than half

Mathematics
1 answer:
Sedaia [141]3 years ago
4 0

Answer:

l = 16 cm

Step-by-step explanation:

Let's set the width of the rectangle as "w" and the length of the rectangle as "w/2 + 9".

The perimeter of a rectangle is calculated by adding up the value of all of its side lengths. Therefore, we can find the perimeter using 2l + 2w = P.

We can substitute 60 for P and w/2 + 9 for l.

  • 2(w/2 + 9) + 2w = 60
  • 2w/2 + 18 + 2w = 60
  • w + 18 + 2w = 60
  • 3w + 18 = 60
  • 3w = 42
  • w = 14

Substitute w = 14 into the equation for length l.

  • l = w/2 + 9
  • l = 14/2 + 9
  • l = 16

The length of the rectangle is 16 cm.

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=================================================================

Work Shown:

The angles A and C are complementary, meaning they add to 90 degrees.

(Angle A) + (Angle C) = 90

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(2x+2x)+(-4+14) = 90

4x+10 = 90

4x+10-10 = 90-10 .... subtract 10 from both sides

4x = 80

4x/4 = 80/4 ..... divide both sides by 4

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If x = 20, then,

angle A = 2x-4 = 2*20-4 = 40-4 = 36 degrees

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Note how A+C = 36+54 = 90 which helps confirm our answers.

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