Given:
The given triangle is a right triangle.
The hypotenuse of the triangle is 40 feet.
The legs of the triangle are 3x feet and 6x feet.
We need to determine the value of x and the side lengths.
Value of x:
The value of x can be determined using the Pythagorean theorem.
Thus, we have;
[tex]40^2=(3x)^2+(6x)^2[/tex]
[tex]1600=9x^2+36x^2[/tex]
[tex]1600=45x^2[/tex]
[tex]35.56=x^2[/tex]
[tex]5.96=x[/tex]
Thus, the value of x is 5.96
Side lengths:
The side lengths can be determined by substituting the value of x.
Thus, we have;
Length 3x = [tex]3(5.96)=17.9 \ ft[/tex]
Length 6x = [tex]6(5.96)=35.8 \ ft[/tex]
Therefore, the side lengths are 17.9 feet and 35.8 feet.
