hamptonlanesha
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Set up an algebraic equation and then solve the following problems.
The length of a rectangle is twice that of its width. If the area of the rectangle is 72 square inches, then find the length and width.

Respuesta :

qabtt

Let's call the length [tex]l[/tex] and the width [tex]w[/tex]. Based on this, we can say:

[tex]l = 2w[/tex]

  • Information given in the problem

[tex]A = lw = (2w)(w) = 2w^2 = 72[/tex]

  • Substitution and simplifying

[tex]2w^2 = 72[/tex]

  • No changes from the previous equation, but focus on this part

[tex]w^2 = 36[/tex]

  • Divide both sides by 2

[tex]w = \pm \sqrt{36} = \pm 6[/tex]

  • Solve for [tex]w[/tex] by finding the square root of both sides of the equation

[tex]w = 6[/tex]

  • [tex]w = -6[/tex] is an extraneous solution because you can't have a negative side length

[tex]l = 2w = 2(6) = 12[/tex]

  • Find the length to complete the problem

The width of the rectangle is 6 inches and the length of the rectangle is 12 in.

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