Problem: The sides of a right triangle are aaa and bbb and the hypotenuse is ccc. A perpendicular from the vertex divides c into segments r and s , adjacent respectively to a and b . If a:b=1:3a: b=1: 3a:b=1:3, then the ratio of rrr to sss is:
Answer Choices:
A. 1:31: 31:3
B. 1:91: 91:9
C. 1:101: 101:10
D. 3:103: 103:10
E. 1:101: \sqrt{10}1:10​ Solution:
a2=crb2=csa^{2}=c r \quad b^{2}=c s a2=crb2=cs
rs=a2b2=19\dfrac{r}{s}=\dfrac{a^{2}}{b^{2}}=\dfrac{1}{9} sr​=b2a2​=91​