Question

the legs of an isosceles triangle have lengths $x + 1$ and $-x + 7$. the base has length $3x - 3$. what is the length of the base?
4
6
3
cannot be determined

Explanation:

Step1: Set up equation for legs

In an isosceles triangle, two legs are equal. So, \(x + 1=-x + 7\).

Step2: Solve for \(x\)

Add \(x\) to both sides: \(x+x + 1=-x+x + 7\), \(2x+1 = 7\).
Subtract 1 from both sides: \(2x+1-1=7 - 1\), \(2x=6\).
Divide by 2: \(x=\frac{6}{2}=3\).

Step3: Find base length

Substitute \(x = 3\) into \(3x-3\).
\(3\times3-3=9 - 3=6\).

Answer:

6