Answer:
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
[tex]x^{2} +4x -96 = 44[/tex] subtract 44 from both sides so it's equal to 0, then factor.
[tex]x^{2} +4x -140 =0[/tex] -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.
