Question

the figure has perimeter p = 74. find the value of x. (type a whole number.) (figure is not to scale.)

Explanation:

Step1: Recall perimeter formula

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. So for a triangle with side - lengths \(x\), \(x + 4\), and \(x+7\), we have \(P=x+(x + 4)+(x + 7)\).

Step2: Simplify the perimeter equation

Combine like - terms: \(x+(x + 4)+(x + 7)=3x+11\).

Step3: Set up the equation with given perimeter

We know that \(P = 74\), so \(3x+11 = 74\).

Step4: Solve for \(x\)

Subtract 11 from both sides of the equation: \(3x+11−11=74 - 11\), which gives \(3x=63\). Then divide both sides by 3: \(\frac{3x}{3}=\frac{63}{3}\), so \(x = 21\).

Answer:

21