Problem: The hypotenuse c and one arm a of a right triangle are consecutive integers. The square of the second arm is:
Answer Choices:
A. ca
B. c/a
C. c+a
D. c−a
E. none of these
Solution:
b2=c2−a2=c2−(c−1)2=2c−1=c+c−1=c+a;
or
b2=c2−a2=(a+1)2−a2=2a+1=a+1+a=c+a;
or
b2=c2−a2=(c+a)(c−a)=c+a since c−a=1.