Question 151683
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?
:
Since we will be using Pythagoras, let the length and width = a & b
;
Perimeter is given so we have:
2a + 2b = 14
Simplify, divide by 2
a + b = 7
or
a = (7-b)
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Enter Pythagoras:
a^2 + b^2 = 5^2
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Substitute (7-b) for a, find b
(7-b)^2 + b^2 = 25
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FOIL (7-b)
49 - 14b + b^2 + b^2 = 25 
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Arrange as a quadratic equation
2b^2 - 14b + 49 - 25 = 0
:
2b^2 - 14b + 24 = 0
Factor:
(2b - 8)(b - 3) = 0
Solutions
2b = 8
b = 4
and
b = 3
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We can use either solution if b=4, then a=3, or vice-versa
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