Question

please help!!! What are the values of a and b?

(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
202+a2=b2
This is by the Pythagorean Theorem.

We also see form the larger outer triangle
292+b2=(21+a)2
Also by the Pythagorean Theorem.

We now have a system of equations to work with.
Substituting
202+a2
in for
b2
in the second equation we have:
292+(202+a2)=(21+a)2
Simplifying the left and right hand sides, we have:
841+400+a2=441+a2+42a

1241+a2=441+a2+42a
now we cancel the (a^2)s and solve for a
1241+a2=441+a2+42a

800=42a

a≈19

Answer 2

so a = 800/42 = 400/21. and b we find by plugging a into the first equation.
b2=202+192
b=(√761)
b≈27.6≈580/21
So the answer is A

Answer 3

thankyou very much. this helped me a lot!

Answer 4

@bob_s. NP (: