Question

a triangle has side lengths of (2b + 5c) centimeters, (10b + 7d) centimeters, and (4d − 3c) centimeters. which expression represents the perimeter, in centimeters, of the triangle? answer
○ 9c + 12b + 4d
○ 12b + 2c + 11d
○ 17bd + 7bc + cd
○ 16bd + 9cd
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Explanation:

Step1: Recall perimeter formula

The perimeter \( P \) of a triangle is the sum of its three side lengths. So, \( P=(2b + 5c)+(10b + 7d)+(4d-3c) \).

Step2: Combine like terms for \( b \)

Combine the terms with \( b \): \( 2b+10b = 12b \).

Step3: Combine like terms for \( c \)

Combine the terms with \( c \): \( 5c-3c = 2c \).

Step4: Combine like terms for \( d \)

Combine the terms with \( d \): \( 7d + 4d=11d \).

Step5: Form the perimeter expression

Putting it all together, the perimeter \( P = 12b+2c + 11d \).

Answer:

\( 12b + 2c + 11d \) (corresponding to the option "12b + 2c + 11d")