Respuesta :
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 √40.
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.
