Answer:
18 inches by 80 inches
Explanation:
The given relations can be used in conjunction with the Pythagorean theorem to find the rectangle dimensions.
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setup
Let x and y represent the width and length of the rectangle, respectively. One of the relations is that between length and width:
y = 2x +44 . . . . . length is 44 more than twice the width
The other relation is described by the Pythagorean theorem. The square of the diagonal is the sum of the squares of the length and width:
x² +y² = (y +2)²
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solution
Expanding the second equation, and subtracting y², we find ...
x² +y² = y² +4y +4
x² = 4y +4
Substituting for y using the first equation gives the quadratic ...
x² = 4(2x +44) +4
x² = 8x +180 . . . . . . . eliminate parentheses
x² -8x +16 = 196 . . . . add 16 -8x to make perfect squares
(x -4)² = 14²
We're only interested in the positive solution, so ...
x = 4 +14 = 18 . . . . . . . . square root, add 4
y = 2(18) +44 = 80
The dimensions of the rectangle are 18 inches wide by 80 inches long.
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Check
The diagonal is √(18² +80²) = √6724 = 82.