Question

Help! I would like a walkthrough of how to do this problem, as i cant figure out how to. Thanks!

Answer 1

Answer:

a = 8, b = 10

Step-by-step explanation:

1. We know the measurements of one half of the triangle.
2. We know that the triangles are a slightly different size but they have one side that is the same length, which measures 6. If we rotated the triangles, 10 would be the same as side b on the smaller triangle.
3. We can represent this with $\frac{10}{b}$, or $\frac{big triangle}{small triangle}$.
4. With the triangles rotated, we know if 10 is the same side as b (b is NOT 10, by the way!) then 8 would be the same side as a ( $\frac{8}{a}$ )
5. So if the third side of both triangles is 6, then we can set up all of this information to figure out what a and b are. How?
6. Well, if $\frac{8}{10}$ = $\frac{a}{b}$ and $\frac{8}{a}$ = $\frac{10}{b}$, then 8b = 10a. What does 8 and 10 both go into? 80! So what would we multiply 8 and 10 by (which would be a and b) to get 80 on both sides?
7. a = 8 because 10 • 8 = 80.
8. b = 10 because 8 • 10 = 80.
9. That would get us 80 = 80, which is not an impossibility! :D

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.