Question

What are the values of A and B

http://i47.tinypic.com/33a73nm.png

A. a = 400/21, b = 580/21
B. a = 400/21, b = 20/21
C. a =580/21, b = 29/21
D. a = 20/21, b=580/21

Answer 1

From the smaller inner triangle we see that \[20^2+a^2=b^2\] This is by the Pythagorean Theorem.

We also see form the larger outer triangle \[29^2+b^2=(21+a)^2\] Also by the Pythagorean Theorem.

We now have a system of equations to work with.
Substituting \[20^2+a^2\] in for \[b^2\] in the second equation we have:
\[29^2+(20^2+a^2)=(21+a)^2\] Simplifying the left and right hand sides, we have:
\[841+400+a^2=441+a^2+42a\]
\[1241+a^2=441+a^2+42a\] now we cancel the (a^2)s and solve for a
\[1241+a^2=441+a^2+42a\]
\[800=42a\]
\[a \approx19\]

Answer 2

oops, let me finish. so a = 800/42 = 400/21. and b we find by plugging a into the first equation. \[b^2=20^2 + 19^2\]\[b=\sqrt(761)\]\[b \approx27.6 \approx 580/21\] So the answer is A

Answer 3

thank you!

Answer 4

no problem!