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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?

Feb 14, 2018

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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)

(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

Feb 14, 2018