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A triangle has side lengths of [tex][tex]$(q+r)$[/tex][/tex] centimeters, [tex][tex]$(5q-10s)$[/tex][/tex] centimeters, and [tex][tex]$(5s-7r)$[/tex][/tex] centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

A. [tex][tex]$-16rs+11qs$[/tex][/tex]
B. [tex][tex]$-2rs+2qr-5qs$[/tex][/tex]
C. [tex][tex]$6q-6r-58$[/tex][/tex]
D. [tex][tex]$6q-2s-9r$[/tex][/tex]



Answer :

GinnyAnswer
To determine the perimeter of the triangle, we will sum the expressions representing the side lengths of the triangle.

1. The first side length is [tex]\( q + r \)[/tex] cm.
2. The second side length is [tex]\( 5q - 10s \)[/tex] cm.
3. The third side length is [tex]\( 5s - 7r \)[/tex] cm.

To find the perimeter, we add these three expressions together:

[tex]\[ \text{Perimeter} = (q + r) + (5q - 10s) + (5s - 7r) \][/tex]

Let's combine like terms from the sum:

- Combine the [tex]\( q \)[/tex] terms: [tex]\( q + 5q \)[/tex] gives [tex]\( 6q \)[/tex].
- Combine the [tex]\( r \)[/tex] terms: [tex]\( r - 7r \)[/tex] gives [tex]\( -6r \)[/tex].
- Combine the [tex]\( s \)[/tex] terms: [tex]\( -10s + 5s \)[/tex] gives [tex]\( -5s \)[/tex].

So, the combined expression is:

[tex]\[ 6q - 6r - 5s \][/tex]

Thus, the perimeter of the triangle, in centimeters, is represented by the expression:

[tex]\[ 6q - 6r - 5s \][/tex]

Among the given multiple-choice options, the correct expression that matches our result is:

[tex]\[ 6q - 6r - 5s \][/tex]

Thus, the answer is:

[tex]\[ \boxed{6q - 6r - 5s} \][/tex]

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