Question

the perimeter of the triangle below is 72 units. find the length of side \\(\overline{vx}\\). write your answer without variables. the triangle has vertices v, w, x. side vx is labeled 5y, side vw is labeled 4y - 1, side wx is labeled y + 3. \\(vx = \square\\)

Explanation:

Step1: Set up the equation for the perimeter

The perimeter of a triangle is the sum of its sides. So, \(5y+(4y - 1)+(y + 3)=72\).
Simplify the left - hand side: \((5y+4y+y)+(-1 + 3)=72\), which gives \(10y+2 = 72\).

Step2: Solve for \(y\)

Subtract 2 from both sides: \(10y=72 - 2\), so \(10y=70\).
Divide both sides by 10: \(y=\frac{70}{10}=7\).

Step3: Find the length of \(VX\)

Since \(VX = 5y\), substitute \(y = 7\) into the expression. Then \(VX=5\times7 = 35\).

Answer:

\(35\)