Problem: The sides of a right triangle are a,a+da, a+da,a+d, and a+2da+2 da+2d, with aaa and ddd both positive. The ratio of aaa to ddd is:
Answer Choices:
A. 1:31: 31:3
B. 1:41: 41:4
C. 2:12: 12:1
D. 3:13: 13:1
E. 3:43: 43:4 Solution:
a2+(a+d)2=(a+2d)2∴a=3d∴ad=31a^{2}+(a+d)^{2}=(a+2 d)^{2} \quad \therefore a=3 d \quad \therefore \dfrac{a}{d}=\dfrac{3}{1} a2+(a+d)2=(a+2d)2∴a=3d∴da​=13​