Answer:
4 cm by 7 cm
Explanation:
The relation between length and width can be used with the area formula to find the dimensions of the rectangle.
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setup
Let x represent the width of the rectangle. Then the length is (3x-5). The area is the product of length and width.
A = LW
28 = (3x -5)(x)
In standard form, this is ...
3x² -5x -28 = 0
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solution
factor
To factor this equation, we are looking for factors of (3)(-28) = -84 that have a total of -5. The factor pairs of -84 are ...
-84 = -84×1 = -42×2 = -28×3 = -21×4 = -14×6 = -12×7
Sums of these pairs are -83, -40, -25, -17, -8, -5.
The last pair, -12×7, gives us a clue as to how to factor the equation.
3x² -5x -28 = (3x -12)(3x +7)/3 = (x -4)(3x +7)
Then the equation we want a solution for is ...
(x -4)(3x +7) = 0
zero product rule
The only positive value of x that makes either factor zero is ...
x = 4
And the other dimension is ...
3x -5 = 3(4) -5 = 7
The rectangle is 5 cm wide and 7 cm long.