Answer:
Shorter leg=3
Longer leg=4
Step-by-step explanation:
Equations
In a right triangle, Pythagora's Theorem is satisfied. Being a the hypotenuse, b and c the legs of the triangle, then:
[tex]a^2=b^2+c^2[/tex]
Let's call
x=the shorter leg of the triangle
The longer leg is 1 cm longer than the shorter leg, thus:
x+1=the longer leg.
Since the hypotenuse is 5 cm long:
[tex]5^2=x^2+(x+1)^2[/tex]
Operating:
[tex]25=x^2+x^2+2x+1[/tex]
Swapping sides and simplifying:
[tex]2x^2+2x+1=25[/tex]
Subtracting 25:
[tex]2x^2+2x-24=0[/tex]
Dividing by 2:
[tex]x^2+x-12=0[/tex]
Factoring:
[tex](x-3)(x-4)=0[/tex]
We have two possible solutions:
x=3, x=4
The longer leg is x+1.
If x=3, x+1=4
If x=4, x+1=5. This solution is not valid because one leg would be equal to the hypotenuse.
Thus, the solution is:
Shorter leg=3
Longer leg=4
