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The side lengths of a quadrilateral are [tex]5x, 7x^3, x^2[/tex], and [tex]10x^2[/tex]. Which expression below gives the perimeter?

A. [tex]23x^4[/tex]

B. [tex]12x^3 + 11x^2[/tex]

C. [tex]7x^3 + 11x^2 + 5x[/tex]

D. [tex]22x^3 + x[/tex]

Answer :

To find the perimeter of a quadrilateral with side lengths [tex]\(5x\)[/tex], [tex]\(7x^3\)[/tex], [tex]\(x^2\)[/tex], and [tex]\(10x^2\)[/tex], we need to add these expressions together.

Let's look at each side length and understand how we can combine them:

1. Side lengths:
- [tex]\(5x\)[/tex]
- [tex]\(7x^3\)[/tex]
- [tex]\(x^2\)[/tex]
- [tex]\(10x^2\)[/tex]

2. Combine like terms:

Now, let's add these expressions:

- Start with [tex]\(7x^3\)[/tex] because it is the only term with [tex]\(x^3\)[/tex].

- Next, combine the terms with [tex]\(x^2\)[/tex]: [tex]\(x^2\)[/tex] and [tex]\(10x^2\)[/tex] add up to [tex]\(11x^2\)[/tex].

- Lastly, include [tex]\(5x\)[/tex] on its own since it is the only term with [tex]\(x\)[/tex].

3. Write the perimeter expression:

The final expression for the perimeter is:
[tex]\[
7x^3 + 11x^2 + 5x
\][/tex]

So, the expression that gives the perimeter of the quadrilateral is [tex]\(7x^3 + 11x^2 + 5x\)[/tex]. Therefore, the correct answer is:

C [tex]\(7x^3 + 11x^2 + 5x\)[/tex]

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