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a. Solve the equatation x^2 - 2x = 24
b. What does this solution mean?
c. The surface of the triangle is 120 square cm. What is the length of AB?
+129899 a. x^2 - 2x = 24 subtract 24 from both sides
x^2 - 2x - 24 = 0 factor
(x - 6) (x + 4) = 0
Setting each factor to 0 and solving for x we get that x = 6 or x = -4
b. Note that the area of the triangle on the right = (1/2)x ( x - 2)
And this is the same area as the one on the left = (1/2)x (x -2)
Adding these we get
(x - 2) [ (1/2)x + (1/2)x] = (x - 2) [ x ] = x^2 - 2x
So......this means that (a) is representing the area of the triangle as 24 units^2
Proof..... using the positive solution found in "a" we have that
(6)^2 -2(6) = 36 - 12 = 24 units^2
c. If the surface area is 120 cm^2
We can solve this
x^2 - 2x = 120 subtract 120 from both sides
x^2 - 2x - 120 = 0 factor
(x - 12) ( x + 10) = 0
Setting each factor to 0 and solving for x we get that x = 12 or x = -10
Taking the positive solution AB = 2x = 2(12) = 24 cm
