Question

identifying components of an expression
clara is building a triangular garden. she wants the length of the longest side to be three more than twice as long as the length of the shortest side, and the third side will be twelve feet long. what expression could she write to determine the perimeter of the triangle if s represents the length of the shortest side? (recall that perimeter is the distance around a shape.)
s + (2s + 3) + 12
what is the expression in simplified form?
s + (2s + 3) + 12
s+ 2s+ 12
s+ (2s+ 3)
3s
what is the coefficient of the variable in the simplified expression?

Explanation:

Step1: Identify side - lengths

The shortest side is \(s\), the longest side is \(2s + 3\), and the third side is 12.

Step2: Calculate perimeter formula

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. So \(P=s+(2s + 3)+12\).

Step3: Simplify the expression

Combine like - terms: \(s+2s=3s\), and \(3 + 12 = 15\). So \(s+(2s + 3)+12=3s+15\). The coefficient of the variable \(s\) in the simplified expression \(3s + 15\) is 3.

Answer:

The perimeter expression is \(s+(2s + 3)+12\), the simplified expression is \(3s + 15\), and the coefficient of the variable in the simplified expression is 3.