contestada

The perimeter of a rectangle is 72 inches. Its length
is 6 inches greater than twice its width. What is the
length of the rectangle?
A 10 inches
B 11 inches
C 26 inches
D 28 inches

Respuesta :

chetankachana

Answer:

26 inches

Step-by-step explanation:

Hi!

Let the length be called L, the width be called W, and the perimeter be called P.

The perimeter of a rectangle is twice the sum of L and W.

  • [tex]P = 2(L+W)[/tex]

We know that the length is 6 inches greater than twice the width, so translating that with the variables we have is: [tex]L = 6 + 2W[/tex]

By substituting values into the equation, we can solve for W.

Solve for W:

  • [tex]P = 2(L + W)[/tex]    
  • [tex]72 = 2(6 + 2W + W)[/tex] --> Substitute values
  • [tex]72 = 2(6 + 3W)[/tex] --> Simplify
  • [tex]36 = 6 + 3W[/tex] --> Divide both sides by 2
  • [tex]30 = 3W[/tex] --> Subtract 6 from both sides
  • [tex]10 = W[/tex] --> Divide both sides by 10

So the width is 10 inches. And since we know that the length is 6 plus twice the width, the length would be...

  • [tex]L = 6 + 2W[/tex]
  • [tex]L = 6 + 2(10)[/tex]
  • [tex]L = 6+20[/tex]
  • [tex]L = 26[/tex]

The length of the rectangle is 26 inches.

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