A rectangle has a length that is 4 meters more than the width. The area of the rectangle is 117 square meters. Find the dimensions of the rectangle.

Answer choices are on picture.

Answer:

Its the first choice. Width:9 Length:13

Step-by-step explanation:

If the length is 4 meter more than the width than that means whatever the width is you must add 4 to it, in this case the width is 9 so add 4 to it which equals 13. If the length matches your answer it is the correct choice.

The area of a rectangle is the product of its dimensions. The dimension of the rectangle is: [tex]Length = 13m[/tex] and [tex]Width = 9m[/tex]

Given that:

[tex]L =4 + W[/tex]

[tex]Area = 117[/tex]

The area of a rectangle is:

[tex]Area = L \times W[/tex]

So, we have:

[tex]L \times W= 117[/tex]

Substitute [tex]L =4 + W[/tex]

[tex](4 + W) \times W = 117[/tex]

Expand

[tex]4W + W^2 = 117[/tex]

Rewrite as:

[tex]W^2 + 4W- 117 = 0[/tex]

Expand

[tex]W^2 + 13W - 9W - 117 = 0[/tex]

Factorize

[tex]W(W + 13) - 9(W + 13) = 0[/tex]

Factor out W + 13

[tex](W - 9)(W + 13) = 0[/tex]

Solve for W

[tex]W = 9[/tex] or [tex]W = -13[/tex]

The dimension cannot be negative.

So:

[tex]W = 9[/tex]

Recall that:

[tex]L =4 + W[/tex]

[tex]L = 4 + 9[/tex]

[tex]L = 13[/tex]

So, the dimension of the rectangle is:

[tex]Length = 13m[/tex]

[tex]Width = 9m[/tex]

Read more about areas at:

https://brainly.com/question/15218510

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