Question

Triangle ABC is shown below. Triangle A B C is shown. The length of side A B is 2 x, the length of side B C is 4 x minus 10, and the length of side A C is 3 x minus 7. Angle A B C and B C A are congruent. What is the length of line segment AC? 7 9 14 18

Answer 1

The answer is 7.
If angels ABC and BCA are congruent, then their opposite sides are congruent (sides AB and AC). Therefore, 3x-7=2x, giving you the answer of 7 when solved.

Answer 2

The length of line segment AC of the given triangle is; 14

How to find the length of the line segment?

Since Angle ABC and BCA are congruent, it means that they are equal.

An isosceles triangle is a triangle that has two equal sides and two equal base angles.

Now, since Angle ABC and BCA are equal, it means that the triangle is an isosceles triangle. It also means that sides AC and AB are equal. The expression becomes;

3x - 7 = 2x

3x - 2x = 7

x = 7

To determine the length of line segment AC. We will substitute x = 7 into 3x - 7. It becomes

(3 × 7) - 7

= 21 - 7 = 14

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