Answer:
Part 1)
a=3; BC=10; AC=10
Part 2)
Isosceles Triangle
Step-by-step explanation:
Part 1)
We know that AC=BC.
Therefore, their lengths are equivalent.
So, we can write the following equation:
[tex]6a-8=4a-2[/tex]
Let’s solve for a. Subtract 4a from both sides:
[tex]2a-8=-2[/tex]
Add 8 to both sides:
[tex]2a=6[/tex]
Divide both sides by 2. Therefore, the value of a is:
[tex]a=3[/tex]
Now, we can substitute the value back to find AC and BC.
For AC, we have:
[tex]AC=6a-8\\[/tex]
Substitute 3 for a:
[tex]AC=6(3)-8=18-8=10[/tex]
So, the value of AC is 10.
For BC, we have:
[tex]BC=4a-2[/tex]
Substitute 3 for a:
[tex]BC=4(3)-2=12-2=10[/tex]
Therefore, both AC and BC measure 10 units, which was expected.
Part 2)
Remember that:
- A triangle is scalene if all three of its sides are different.
- A triangle is isosceles if two of its sides are equal.
- And a triangle is equilateral when all of its sides are equal.
We know that AC is equal to BC. So, two sides are equal.
We don’t know anything about AB. AB could or could not be equal.
Therefore, the best answer is that Triangle ABC is an isosceles triangle.
