type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar…

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

Answer

Explanation:

Step1: Set up perimeter equation

The perimeter of a triangle is the sum of its side - lengths. For this isosceles triangle, the perimeter $P=(x - 1)+(x - 1)+x$. Given that $P = 13$, we have the equation $(x - 1)+(x - 1)+x=13$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x-1+x - 1+x=3x-2$. So, $3x-2 = 13$.

Step3: Solve for x

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

Step4: Find the side - lengths

The length of the longest side is $x$ inches, and the other two equal sides are $x - 1$ inches. Substitute $x = 5$ into the expressions. The longest side is $x=5$ inches, and the other two sides are $x - 1=5 - 1 = 4$ inches.