Prove that any median in a triangle is less than the half of the triangle's perimeter.
1 answer:
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.
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Answer:
A. The solutions are .
B. The factored form of the quadratic expression
Step-by-step explanation:
A. To find the solutions to the quadratic equation you must:
The solutions are:
B. Two expressions are equivalent to each other if they represent the same value no matter which values we choose for the variables.
To factor :
First, multiply the constant in the polynomial by where
is equal to -1.
Since both terms are perfect squares, factor using the difference of squares formula