Question

32 write an expression that represents the perimeter of triangle. combine like terms.
(image of a triangle with two sides labeled 3x and base labeled 15)
perimeter of triangle blank
if the perimeter of the triangle is 90, what is the value of x?
x = blank

Explanation:

Step1: Recall perimeter formula

Perimeter of a triangle is the sum of its three sides. The sides are \(3x\), \(3x\), and \(15\). So the perimeter \(P = 3x + 3x + 15\).

Step2: Combine like terms

Combine the \(3x\) terms: \(3x + 3x = 6x\), so the perimeter expression is \(6x + 15\).

Step3: Solve for \(x\) when \(P = 90\)

Set the perimeter expression equal to 90: \(6x + 15 = 90\). Subtract 15 from both sides: \(6x = 90 - 15 = 75\). Then divide both sides by 6: \(x=\frac{75}{6}=\frac{25}{2}=12.5\).

Answer:

Perimeter expression: \(6x + 15\); Value of \(x\): \(12.5\) (or \(\frac{25}{2}\))