Answer:
A. Between 14 and 15.
Step-by-step explanation:
Let x be the one leg of the right triangle.
We have been given that the legs of a right triangle are in the ratio of 3 to 1. So, the other leg of the right triangle would be 3x.
We are also told that the length of the hypotenuse of the triangle is β40.
Using Pythagoras theorem, we can set am equation as:
[tex]x^2+(3x)^2=(\sqrt{40})^2[/tex]
Let us solve for x.
[tex]x^2+9x^2=40[/tex]
[tex]10x^2=40[/tex]
[tex]\frac{10x^2}{10}=\frac{40}{10}[/tex]
[tex]x^2=4[/tex]
Take square root of both sides:
[tex]x=\sqrt{4}[/tex]
[tex]x=2[/tex]
The other leg would be [tex]3x\Rightarrow 3\cdot 2=6[/tex].
The perimeter of the triangle would be:
[tex]\text{Perimeter of triangle}=2+6+\sqrt{40}[/tex]
[tex]\text{Perimeter of triangle}=2+6+6.324555[/tex]
[tex]\text{Perimeter of triangle}=14.324555[/tex]
Therefore, the perimeter of the triangle is between 14 and 15 and option A is the correct choice.