Answer:
The length of the shorter leg is 12 cm
The length of the longer leg is 35 cm
The length of the hypotenuse is 37 cm
Step-by-step explanation:
Let
x ----> the length of the shorter leg
y ----> the length of the longer leg
z ----> the length of the hypotenuse
we know that
----> equation A
----> equation B
Remember that in a right triangle we can apply the Pythagorean Theorem
so
----> equation C
substitute equation A and equation B in equation C
![(3x+1)^2=x^2+(3x-1)^2](https://tex.z-dn.net/?f=%283x%2B1%29%5E2%3Dx%5E2%2B%283x-1%29%5E2)
solve for x
![9x^2+6x+1=x^2+9x^2-6x+1](https://tex.z-dn.net/?f=9x%5E2%2B6x%2B1%3Dx%5E2%2B9x%5E2-6x%2B1)
simplify
![6x=x^2-6x](https://tex.z-dn.net/?f=6x%3Dx%5E2-6x)
![x^2-12x=0](https://tex.z-dn.net/?f=x%5E2-12x%3D0)
![x(x-12)=0](https://tex.z-dn.net/?f=x%28x-12%29%3D0)
The solutions are x=0 cm, x=12 cm
therefore
The solution is x=12 cm
<em>Find the value of y</em>
![y=3(12)-1=35\ cm](https://tex.z-dn.net/?f=y%3D3%2812%29-1%3D35%5C%20cm)
<em>Find the value of z</em>
![z=3(12)+1=37\ cm](https://tex.z-dn.net/?f=z%3D3%2812%29%2B1%3D37%5C%20cm)
therefore
The length of the shorter leg is 12 cm
The length of the longer leg is 35 cm
The length of the hypotenuse is 37 cm