High School

The width of a rectangle measures [tex](s + 5t)[/tex] centimeters, and its length measures [tex](s + 2)[/tex] centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?

A. [tex]14t + 4s[/tex]
B. [tex]7 + 2s[/tex]
C. [tex]5 + 4s + 4t[/tex]
D. [tex]14 + 4s[/tex]

Answer :

To determine the expression for the perimeter of a rectangle given its dimensions, let's break it down step by step.

1. Identify the Dimensions:
- The width of the rectangle is given as [tex]\((s + 5t)\)[/tex] centimeters.
- The length of the rectangle is given as [tex]\((s + 2)\)[/tex] centimeters.

2. Formula for Perimeter:
- The formula for the perimeter [tex]\(P\)[/tex] of a rectangle is:
[tex]\[
P = 2 \times (\text{width} + \text{length})
\][/tex]

3. Substitute the Given Expressions:
- Substitute the expressions for width and length into the perimeter formula:
[tex]\[
P = 2 \times ((s + 5t) + (s + 2))
\][/tex]

4. Simplify Inside the Parentheses:
- Combine like terms inside the expression:
[tex]\[
(s + 5t) + (s + 2) = 2s + 5t + 2
\][/tex]

5. Calculate the Perimeter:
- Multiply the simplified expression by 2:
[tex]\[
P = 2 \times (2s + 5t + 2) = 4s + 10t + 4
\][/tex]

Thus, the expression that represents the perimeter of the rectangle in centimeters is [tex]\(4s + 10t + 4\)[/tex].

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