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 legs opposite the equal angles are equal. So, \(3x - 5=2x\).

Step2: Solve the equation for \(x\)

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

Step3: Find the lengths of the sides

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

Answer:

The value of \(x\) is \(5\), the length of the top - left side is \(10\), and the length of the bottom - left side is \(10\).