Question

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? the length of the longest slide is inches. the other two sides will each be inches in length.

Explanation:

Step1: Set up the equation

The sum of the lengths of the sides of the triangle is equal to the length of the rod. So, \(x+(x - 1)+(x - 1)=13\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+x - 1+x - 1=3x-2\). The equation becomes \(3x-2 = 13\).

Step3: Solve for \(x\)

Add 2 to both sides of the equation: \(3x-2+2=13 + 2\), which simplifies to \(3x=15\). Then divide both sides by 3: \(x=\frac{15}{3}=5\).

Answer:

The length of the longest side is \(5\) inches. The other two sides will each be \(x - 1=5 - 1 = 4\) inches.