Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. an instrument maker creates a triangle in the shape of an isosceles triangle by bending a metal rod. the rod is 13 inches long, and the bottom of the triangle is longer than the two sides. what is the length of the longest side? diagram of isosceles triangle with two sides labeled ( x - 1 ) in and base labeled ( x ) in the length of the longest side is (\boxed{quad}) inches. the other two sides will each be (\boxed{quad}) inches in length. reset next

Explanation:

Step1: Set up the equation for the perimeter

The perimeter of the isosceles triangle is the sum of its three sides. The two equal sides are \(x - 1\) inches each, and the base is \(x\) inches. The total length of the rod (perimeter) is 13 inches. So we have the equation: \((x - 1)+(x - 1)+x = 13\)

Step2: Simplify and solve the equation

First, combine like terms: \(x - 1+x - 1+x=13\) simplifies to \(3x - 2 = 13\). Then, add 2 to both sides: \(3x=13 + 2=15\). Next, divide both sides by 3: \(x=\frac{15}{3}=5\)

Step3: Find the length of the equal sides

Substitute \(x = 5\) into the expression for the equal sides (\(x - 1\)): \(5-1 = 4\)

Answer:

The length of the longest side is \(\boldsymbol{5}\) inches. The other two sides will each be \(\boldsymbol{4}\) inches in length.