Question

a triangle has side lengths of (6g + 10) centimeters, (5g − 7) centimeters, and (2h − 10) centimeters. which expression represents the perimeter, in centimeters, of the triangle?

answer
○ −8h + 16g − 2
○ −7 + 11g + 2h
○ 11g + 3 − 8h
○ −8h + 14g
submit answer

Explanation:

Step1: Recall perimeter formula

The perimeter \( P \) of a triangle is the sum of its three side lengths. So, \( P=(6g + 10)+(5g - 7)+(2h - 10) \).

Step2: Combine like terms for \( g \)

Combine the terms with \( g \): \( 6g+5g = 11g \).

Step3: Combine constant terms

Combine the constant terms: \( 10-7 - 10=10 - 17=-7 \).

Step4: Include the term with \( h \)

The term with \( h \) is \( 2h \). So putting it all together, \( P = 11g+2h-7=-7 + 11g+2h \).

Answer:

\(-7 + 11g + 2h\) (corresponding to the option \(-7 + 11g + 2h\))