Answer:
6.3 units
Step-by-step explanation:
We let x be the length of the shorter leg.
This implies that the length of other leg in terms of x is 3x , as shown in the image.
Using Pythagorean Theorem, we can find the value of x.
This implies that,
[tex]{x}^{2} + {(3x)}^{2} ={20}^{2} [/tex]
[tex] \implies{x}^{2} +9{x}^{2} =400[/tex]
[tex] \implies10{x}^{2} =400[/tex]
We divide through by 10
[tex] \implies \frac{10 {x}^{2}}{10} = \frac{400}{10} [/tex]
[tex] \implies{x}^{2}=40[/tex]
Taking positive square root of both sides,we obtain;
[tex]x = \sqrt{40} [/tex]
[tex] \implies x = 6.3 units[/tex]
