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Tresset [83]
3 years ago
6

A rectangle is 6 inches longer than it is wide. The perimeter of the rectangle is 44 inches.Write and solve an equation for the

length and width of the rectangle.
Mathematics
1 answer:
Nataly_w [17]3 years ago
5 0

Answer:

Length is 14 in

Width is 8 in

Step-by-step explanation:

<u>Given:</u>

  • Length = l
  • Width = w
  • Perimeter = P = 44 in
<h3>Solution</h3>

<u>Equations as per given:</u>

  • l - w = 6
  • P= 2(l+w) = 44 ⇒ l +w = 22

<u>Adding up the two equations:</u>

  • l - w  + l +w = 6 + 22
  • 2l = 28
  • l = 28/2
  • l = 14 in

<u>Then finding the value of w:</u>

  • w = l -6
  • w = 14 - 6
  • w = 8 in

<u>Answer:</u> The length of the rectangle is 14 inches and width is 8 inches

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Step-by-step explanation:

The Law of Sines can be used to find a missing side length in a triangle where the angles are known and at least one side is given. It tells you the ratio of side lengths is equal to the ratio of the sines of their opposite angles. In effect, longer sides are opposite larger angles.

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<h3>compare angles</h3>

The given side length (DE=3) is opposite given angle F=50°. The unknown side length EF is opposite larger angle D=75°.

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Since the unknown side is opposite a larger angle than the other angle given, the length of the unknown side will be longer than the side given.

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<em>Additional comment</em>

If you want to do the actual computation, we have ...

  EF/sin(D) = DE/sin(F)

  EF = DE·sin(D)/sin(F) = 3·sin(75°)/sin(50°) ≈ 3.7828

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