Problema Solution
Two pieces of a large wooden puzzle fit together to form a rectangle with a length 3 centimeters less than twice the width. The diagonal, where the two pieces meet, is 7.5 centimeter in length. Find the length and width of the rectangle.
Answer provided by our tutors
Let
x = the width of the rectangle, x>0
2x - 3 = the length of the rectangle, 2x - 3 >0, x>3/2
d = 7.5 cm the diagonal
Using the Pythagorean Theorem we have:
(2x - 3)^2 + x^2 = d^2
(2x - 3)^2 + x^2 = 7.5^2
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click here to see the equation solved for x
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x = 9/2 cm
x = 4.5 cm
2x - 3 = 2*4.5 - 3 = 6 cm
The length of the rectangle is 6 cm.
The width of the rectangle is 4.5 cm.