Prove that any median in a triangle is less than the half of the triangle's perimeter.

See image for naming of the sides: the medians are

ab, bc, and ac; and sides are a, b, and c

Pick one median, say, ab. The following are true:

ab < a

ab < b

->

ab + ab < a + b

ab < 0.5*(a+b)     | add 0.5*c to the right hand side (does not change inequality)

ab < 0.5(a+b+c) = half perimeter

so ab < half perimeter

Same argument for bc, and ac holds.

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.

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step-by-step explanation: