So, let's do the first problem!
If \(RG'\) is 12 and\(G'G\) is 3, then \(RG\) is 15 because \(12+3=15\) .
\(RG'/RG = 12/15 = 4/5\)
Therefore, the scale factor is 4/5, or C.
Why would you need an altitude, AAS Congruence, or any similar triangles? All you need is substitution in the Pythagorean Theorem, or answer A.
The triangles are similar, so we set up the ratio \(18/y=10.8/18\) and cross-multiplying we get \(324=10.8y\).
Simplifying for \(y \) we get \(y=30\) so the answer is D.
You are very welcome!
The answer to the second one is "B"....this will divide the larger right triangle into two smaller similar right triangles which can be used to prove the P Theorem
For the last one......we have this relationship
y - 10.8 14.4
______ = ______ cross-multiply
10.8 ( y - 10.8) = 14.4 * 14.4
10.8 y - 116.64 = 207.36 add 116.64 to both sides
10. 8 y = 324 divide both sides by 10.8
y = 30