Question

amaya is asked to find the side lengths of the triangle shown. what is her error? for an isosceles triangle, a leg is congruent to the top left side is , and the length of the bottom left side is a leg is not necessarily congruent to the correct solution found by solving the equation is x = the length of (type integers or decimals.) from the top leg and the base, 2x = 6, so x = 3. substitute x into the expression for the bottom legs length to get 3(3) - 5 = 4.

Explanation:

Step1: Identify congruent sides

In an isosceles triangle, the two legs are congruent. So we set up the equation \(2x-5 = 2x\), which is incorrect. The correct equation should be \(2x-5=6\) since the non - variable side is likely the base and the two expressions with \(x\) represent the legs.

Step2: Solve the correct equation

\[

$$\begin{align*} 2x-5&=6\\ 2x&=6 + 5\\ 2x&=11\\ x&=\frac{11}{2}=5.5 \end{align*}$$

\]

Step3: Find side lengths

The length of the legs: Substitute \(x = 5.5\) into \(2x-5\) or \(2x\). For \(2x-5\), we have \(2\times5.5-5=11 - 5=6\). For \(2x\), we have \(2\times5.5 = 11\). The base length is \(6\).
The top left side (leg) length: \(2x-5\), substituting \(x = 5.5\) gives \(6\). The bottom left side (base) length is \(6\).
The correct \(x\) value is \(5.5\).

Answer:

The top left side is \(6\), the length of the bottom left side is \(6\), \(x = 5.5\)