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 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.
(type integers or decimals.)

Explanation:

Step1: Analyze the property of isosceles triangle

In an isosceles triangle, the two legs are congruent. Amaya wrongly set the top - leg (\(2x\)) equal to the base (\(6\)). She should set the two legs (\(2x\) and \(3x - 5\)) equal to each other.

Step2: Solve the equation for \(x\)

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

Step3: Find the lengths of the legs

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

Answer:

Amaya's error was equating the leg (\(2x\)) to the base (\(6\)) instead of equating the two legs (\(2x\) and \(3x - 5\)). The lengths of the two legs are \(10\) and \(10\).