A composite figure is formed by combining a square and a triangle. Its total area is 50.5 ft2. The area of the triangle is 41.5 ft2. What is the length of each side of the square? Complete the explanation. The area of the square is ft2, so each side of the square is ft.

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11 10x0.000000000092^11

by algebra, we combine the fractions: c + 1/c = c²/c + 1/c = (c²+1)/c ≥ 2.

(c²+1)/c ≥ 2 and we multiply both sides by c. c is positive so inequality sign stay s.

c² + 1 ≥ 2c ⇔ c²-2c + 1 = (c - 1)(c - 1) ≥ 0

consider case where 0 < c < 1. by the subtraction property of equality, subtracting through by 1, we have

-1 < c - 1 < 0

so c - 1 is negative for 0 < c < 1. but (c - 1)(c - 1)   means that we have a negative times a negative which is a positive. thus (c - 1)(c - 1) ≥ 0 is true for 0 < c < 1.

consider case where c = 1. then (1-1)(1-1) = 0 ≥ 0 which is true

consider the case where c > 1. by the subtraction property of equality, this is equivalent to c - 1 > 0. so c - 1 is a positive number, and (c-1)(c-1) is positive, thereby satisfying (c - 1)(c - 1) ≥ 0.

so c + 1/c ≥ 2 is true for all c > 0.