Problem: If the perimeter of a rectangle is p and its diagonal is d, the difference between the length and width of the rectangle is:
Answer Choices:
A. 28d2−p2
B. 28d2+p2
C. 26d2−p2
D. 26d2+p2
E. 48d2−p2
Solution:
l2+w2=d2,l+w=p/2,(l+w)2=l2+2lw+w2=p2/4, 2lw=p2/4−d2,(l−w)2=l2−2lw+w2=2d2−p2/4, and l−w=8d2−p2/2.