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 attempt 1 out of 2
9c + 12b + 4d
12b + 2c + 11d
17bd + 7bc + cd
16bd + 9cd

Explanation:

Step1: Recall perimeter formula

Perimeter of a triangle is the sum of its three sides. So, we need to add \((2b + 5c)\), \((10b + 7d)\), and \((4d - 3c)\).

Step2: Combine like terms

First, add the terms with \(b\): \(2b+10b = 12b\).
Then, add the terms with \(c\): \(5c-3c = 2c\).
Next, add the terms with \(d\): \(7d + 4d=11d\).
Now, combine these results: \(12b + 2c+11d\).

Answer:

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