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: Use the property of isosceles triangle

In an isosceles triangle, the two legs are congruent. So, we should set \(3x - 5=2x\) (not \(2x = 6\) as Amaya did).

Step2: Solve the equation \(3x - 5=2x\)

Subtract \(2x\) from both sides: \(3x-2x - 5=2x-2x\), which gives \(x - 5=0\).
Then add 5 to both sides: \(x-5 + 5=0 + 5\), so \(x = 5\).

Step3: Find the lengths of the sides

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

Answer:

Amaya's error is that she wrongly assumed the base (\(6\)) was equal to one of the legs (\(2x\)). In an isosceles triangle, the two legs are congruent. The correct value of \(x\) is \(5\), the length of the top - left side is \(10\), and the length of the bottom - left side is \(10\).