Suppose you transform a square by increasing one side by 12 units and decreasing the other side by 8 units. If the area of the resulting rectangle equals 44 how many units long was the side of the original square?

The the side of the original square is 10 units

Step-by-step explanation:

Take the facts given to set up an equation:

(x +12)(x-8) = 44  Foil and create a quadratic equation

  subtract 44 from both sides so it's equal to 0, then factor.

 -10 × 14 satisfies product of 140 and difference of 4

(x + 14)(x - 10) =0  Set each factor equal to 0, and solve for x

x + 14 =0  x = -14 not viable as real polygons cant have negative side values.

x - 10 = 0  x = 10 This works.

Prove by substituting in original equation

(10 + 12)(10 - 8) = 44   22 × 2 = 44  True!

The original square was 10 x 10 units.

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step-by-step explanation: