Respuesta :
Shorter leg = x
Longer leg = x +1
Length of the hypotenuse: 5 m
We can use the pythagorean theorem with the information given. Doing so, we have:
[tex]\begin{gathered} a^2+b^2=c^2 \\ (x)^2+(x+1)^2=5^2\text{ (Replacing the values)} \\ x^2+x^2+2x+1=25\text{ (Raising both terms to the power of 2)} \\ x^2+x^2+2x=25-1\text{ (Subtracting 1 from both sides of the equation)} \\ 2x^2+2x=24\text{ (Adding like terms)} \\ 2x^2+2x\text{ }-24=0\text{ (Subtracting 24 from both sides of the equation)} \\ 2(x+4)(x-3)=0\text{ (Factoring)} \\ x1=-4\text{ (Since x=-4 makes the factor (x+4) equal to 0)} \\ x2=3\text{ (Since x=3 makes the factor (x}-3\text{) equal to 0)} \\ \text{ Since we need a positive solution x would be equal to 3} \end{gathered}[/tex]So, the answers would be:
Shorter leg = 3 m
Longer leg = 4 m
Length of the hypotenuse: 5 m
