Question

amaya is asked to find the side lengths of the triangle shown. what is her error? 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. for an isosceles triangle, a leg is congruent to a leg is not necessarily congruent to the correct solution found by solving the equation is x = the length of the top left side is, and the length of the bottom left side is

Explanation:

Step1: Identify the property of isosceles triangle

In an isosceles triangle, the sides opposite equal angles are equal. Here, the two angles are equal, so the sides opposite them ( \(2x\) and \(3x - 5\) ) should be set equal, not \(2x\) and \(6\).

Step2: Solve the correct equation

Set \(2x=3x - 5\).
Subtract \(2x\) from both sides: \(0=x - 5\).
Add \(5\) to both sides: \(x = 5\).

Step3: Find the side lengths

For the top - left side (\(2x\)): substitute \(x = 5\), \(2\times5=10\).
For the bottom - left side (\(3x - 5\)): substitute \(x = 5\), \(3\times5-5=15 - 5=10\).

Answer:

For an isosceles triangle, a leg is congruent to the other leg. A leg is not necessarily congruent to the base. The correct solution found by solving the equation \(2x=3x - 5\) is \(x = 5\). The length of the top - left side is \(10\), and the length of the bottom - left side is \(10\).