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 the legs equal

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

Step2: Solve for \(x\)

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

Step3: Find the length of the base

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

Answer:

6