Answer:
a = 8, b = 10
Step-by-step explanation:
- We know the measurements of one half of the triangle.
- 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.
- We can represent this with [tex]\frac{10}{b}[/tex], or [tex]\frac{big triangle}{small triangle}[/tex].
- 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 ( [tex]\frac{8}{a}[/tex] )
- 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?
- Well, if [tex]\frac{8}{10}[/tex] = [tex]\frac{a}{b}[/tex] and [tex]\frac{8}{a}[/tex] = [tex]\frac{10}{b}[/tex], 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?
- a = 8 because 10 • 8 = 80.
- b = 10 because 8 • 10 = 80.
- 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.
