Answer:
The side lengths are 17.9 feet and 35.8 feet
Step-by-step explanation:
Given lengths are;
40 feet, 3x feet and 6x feet
As the given triangle is right angled,
a = 3x, b = 6x and c = 40
Using Pythagorean theorem;
[tex]a^2+b^2=c^2\\(3x)^2+(6x)^2=(40)^2\\9x^2+36x^2=1600\\45x^2=1600\\[/tex]Dividing both sides by 45
[tex]\frac{45x^2}{45}=\frac{1600}{45}\\x^2=35.55[/tex]
Taking square root on both sides
[tex]\sqrt{x^2}=\sqrt{35.55}\\x=5.96[/tex]
Side lengths = 3x = 3(5.96) = 17.9 feet
and
6x = 6(5.96) = 35.8 feet
Hence,
The side lengths are 17.9 feet and 35.8 feet
