The legs of a right triangle are in the ratio of 3 to 1. if the length of the hypotenuse of the triangle is 40√40, then the perimeter of the triangle is between

a. 14 and 15
b. 13 and 14
c. 12 and 13
d. 11 and 12
e. 10 and 11

So then the best option on this case is:

A. 14 and 15

Step-by-step explanation:

When we have a right triangle we can use the Pythegorean identity given by:

 (1)

Where Hip represent the hypothenuse. Opp represent the opposite side and Adj the adjacent side.

On this case we have given the hypothenuse assumed because is the only possible reasonable value because is a too much higher value

We have a ratio provided on this case, let's assume that the ratio is:

If we rpelace this condition into equation (1) we got:

And then we have this:

And then the opposite side is:

The perimeter is defined as the sum of all the sides, we can find the perimeter like this:

And replacing the values that we found we got:

So then the best option on this case is:

A. 14 and 15