Question

find the perimeter of the triangle.
the perimeter is
inches.

Explanation:

Step1: Identify the triangle type

Since two angles are marked as equal, it is an isosceles triangle. So, \(4x + 1=x + 4\).

Step2: Solve for \(x\)

\(4x+1=x + 4\)
\(4x-x=4 - 1\)
\(3x=3\)
\(x = 1\)

Step3: Find the lengths of the sides

Substitute \(x = 1\) into the side - length expressions:

• One side: \(4x+1=4\times1 + 1=5\) inches
• Another side: \(x + 4=1+4 = 5\) inches
• The third side is \(7\) inches

Step4: Calculate the perimeter

Perimeter \(P=5 + 5+7\)
\(P=17\) inches

Answer:

\(17\)