If the lengths of two sides of a right triangle are 5 and 12 units, what is the least possible length, in units, of the third side? Express your answer in simplest radical form.

(leg)^2 + (leg)^2 = (hypotenuse)^2

(5)^2 + (12)^2 = (h)^2

25 + 144 = (h)^2

169 = (h)^2

sqrt{169} = sqrt{(h)^2}

-13 = h

13 = h

We reject h = -13 because length is a distance and distance cannot be negative.

So, h = 13 units is the answer.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: