A triangle has side lengths of left parenthesis, r, minus, 10, s, right parenthesis(r−10s) centimeters, left parenthesis, 3, r, plus, 2, t, right parenthesis(3r+2t) centimeters, and left parenthesis, 2, t, minus, 6, s, right parenthesis(2t−6s) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer

To find the perimeter of the triangle, we simply add the lengths of all three sides. The side lengths are given as:

1. \( (r - 10s) \) cm
2. \( (3r + 2t) \) cm
3. \( (2t - 6s) \) cm

The perimeter \( P \) of the triangle is the sum of these side lengths:

\[
P = (r - 10s) + (3r + 2t) + (2t - 6s)
\]

Now, let's combine like terms:

1. For \( r \)-terms: \( r + 3r = 4r \)
2. For \( s \)-terms: \( -10s - 6s = -16s \)
3. For \( t \)-terms: \( 2t + 2t = 4t \)

So, the perimeter expression simplifies to:

\[
P = 4r - 16s + 4t
\]

Thus, the expression for the perimeter of the triangle is:

\[
P = 4r - 16s + 4t
\]

Would you like to go into more detail, or do you have any further questions?

Here are 5 related questions to explore this topic further:
1. What are the properties of a triangle with variable side lengths?
2. How do you solve for the perimeter if the values of \(r\), \(s\), and \(t\) are known?
3. Can you use this formula to determine if the triangle is valid for certain values of \(r\), \(s\), and \(t\)?
4. How would you calculate the area of this triangle if you knew its height?
5. What happens to the perimeter if one of the side lengths changes proportionally?

**Tip**: Always remember to simplify expressions by combining like terms to avoid errors and to make calculations more efficient.

A triangle has side lengths of (r - 10s) centimeters, (3r + 2t) centimeters, and (2t - 6s) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Discover how to calculate the perimeter of a triangle with side lengths given by algebraic expressions. This problem teaches students to simplify expressions and combine like terms, suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation