Points A, B, and Care collinear, Point B is between A and C. Solve for x,
Find x if AB = x +3, AC = 11, and BC = x.

Explanation:

Saying "Points A,B, and C are collinear" means the three points all fall on the same line. For the sake of simplicity, assume the line is horizontal.

Since B is between A and C, we know that the order of the points from left to right is A, B, C.

Through the segment addition postulate, we say,

AB+BC = AC

(x+3) + (x) = 11

x+3+x = 11

2x+3 = 11

2x = 11-3

2x = 8

x = 8/2

x = 4

Extra info:

Using x = 4, we see that

AB = x+3

AB = 4+3

AB = 7

Note how this adds to BC = x = 4, getting us,

AB+BC = 7+4 = 11

which is the length of segment AC. This confirms AB+BC = AC is true and confirms our answer.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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