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

Explanation:

Step1: Set up perimeter equation

The total length of the rod is the perimeter of the triangle, so:
$$x + 2(x-1) = 13$$

Step2: Simplify the equation

Expand and combine like terms:
$$x + 2x - 2 = 13$$
$$3x - 2 = 13$$

Step3: Solve for $x$

Isolate the variable and calculate:
$$3x = 13 + 2$$
$$3x = 15$$
$$x = \frac{15}{3} = 5$$

Step4: Find equal side length

Substitute $x$ into $x-1$:
$$x-1 = 5-1 = 4$$

Step5: Verify longest side

Compare $x=5$ and $x-1=4$; 5 is longer.

Answer:

The length of the longest side is 5 inches. The other two sides will each be 4 inches in length.