SOLUTION: the perimeter of a notebook is 28 inches and the diagonal measures 10 inches. What are the length and width of the notebook?

Question 255182: the perimeter of a notebook is 28 inches and the diagonal measures 10 inches. What are the length and width of the notebook?

Found 2 solutions by rfer, CharlesG2:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
This is one of those squares, no math needed
6 in by 8 in
most test have a 3 4 5 type triangle just to see if you know what you are doing.
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
the perimeter of a notebook is 28 inches and the diagonal measures 10 inches. What are the length and width of the notebook?
perimeter P = 28
P=2 * (length s + width w) = 28
P=2(s+w)=28
s+w=14
w=14-s
length s ^2 + width w ^2 = 10^2 =100
s^2+w^2=100
s^2+(14-s)^2=100
s^2+196-28s+s^2=100
2s^2-28s+196=100
s^2-14s+98=50
s^2-14s+48=0
(s-6)(s-8)=0
s=6 or s=8
so
w=14-s --> w=8 or w=6
and 36+64=64+36=100
length and width of the notebook is 6 inches and 8 inches

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