Question

amaya is asked to find the side lengths of the triangle shown. what is her error? 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 isosceles - triangle property

In an isosceles triangle, a leg is congruent to another leg, not necessarily to the base. Amaya wrongly assumed the top - leg was congruent to the base to get $2x=6$.

Step2: Set up the correct equation

If the two legs are congruent, we set up the equation $2x = 3x - 5$.

Step3: Solve the equation

Subtract $2x$ from both sides: $0=3x - 2x-5$, which simplifies to $x = 5$.

Step4: Find side - lengths

The length of the top - left side (which is $2x$) is $2\times5=10$. The length of the bottom - left side (which is $3x - 5$) is $3\times5 - 5=10$.

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 $10$.