Question

1. the length of the base on an isosceles triangle is 2x. the length of a leg is 3x + 2. the perimeter of the triangle is 68. find the length of the base.

Explanation:

Step1: Set up the perimeter equation

In an isosceles triangle, two sides (legs) are equal. The perimeter \(P\) of a triangle is \(P=\text{base}+\text{leg}_1+\text{leg}_2\). Given base \( = 2x\), leg \(=3x + 2\), and \(P = 68\). So, \(2x+(3x + 2)+(3x + 2)=68\).

Step2: Simplify the equation

Combine like - terms: \(2x+3x+3x+2 + 2=68\), which gives \(8x+4 = 68\).

Step3: Solve for \(x\)

Subtract 4 from both sides: \(8x=68 - 4=64\). Then divide both sides by 8: \(x=\frac{64}{8}=8\).

Step4: Find the base length

Since the base length is \(2x\), substitute \(x = 8\) into \(2x\). So, base \(=2\times8 = 16\).

Answer:

16