SOLUTION: The perimeter of the cover of an address book is 14 inches, and the diagonal measures 5 inches. What are the length and width of the cover?

Question 215277: The perimeter of the cover of an address book is 14 inches, and the diagonal measures 5 inches. What are the length and width of the cover?
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
perimeter = 2l +2w =14
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l+w=7,,,or w=7-l
.
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diagonal ^2 = l^2 + w^2= 5^2 =25,,,,,subst
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l^2 +(7-l)^2 =25
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l^2 +49 -14l +l^2 = 25
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2l^2 -14l +24 =0,,,,,divide by 2
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l^2 -7l +12 = 0,,,,,factor
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(l-4)(l-3) = 0
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l=4,3,,,,,and w= 3,4
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or conventionally (w smaller) w=3,l=4
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check ,,,,dia = 5 = sqrt{ 3^2 +4^2} ,,,,,ok
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per = 2(3+4)= 14,,,,,,ok
,
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