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. (type integers or decimals.)

Explanation:

Step1: Analyze the properties of an isosceles triangle

In an isosceles triangle, the two legs are congruent. Amaya wrongly assumed that a leg is congruent to the base.

Step2: Set up the correct equation

Since the two legs are congruent, we set up the equation \(2x = 3x - 5\).

Step3: Solve the equation

Subtract \(2x\) from both sides: \(0=x - 5\). Then add \(5\) to both sides: \(x = 5\).

Step4: Calculate the side lengths

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

Answer:

For an isosceles triangle, a leg is congruent to another 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 \(10\).