Question

Can someone teach me how to do these please?
http://imageshack.us/photo/my-images/19/4619582152011124526pm64.png/
What are the values of a and b?

Answer 1

I really need help, I can't find this in the book.

Answer 2

No, this is proportions

Answer 3

That's a similar triangles problem, though it also tests your spatial reasoning skills. The first thing to recognize is that the 6:8:10 triangle is similar to the b:10:a+8 triangle. Then you just figure out the proportions.

For b, \[\frac{6}8 = \frac{b}{10}\]\[8b=60\]\[b=7\frac{1}{2}\]
For a, \[\frac{8}{10}=\frac{10}{a+8}\]\[100=8a+64\]\[36=8a\]\[a=4\frac{1}{2}\]
Checking our work with Pythagorean Theorem,
\[b^2+10^2=(8+a)^2\]\[(7.5)^2+10^2=12.5^2\]\[56.25+100=156.25\checkmark\]

Answer 4

Thank you, I believe I get this now.