Respuesta :
Answer:
Shorter leg: 27 cm,
Longer leg: 36 cm,
Hypotenuse: 45 cm.
Step-by-step explanation:
Let x represent longer leg of the triangle.
We have been given that the shorter leg of a right triangle 9 cm is shorter than the longer leg. This means that the shorter leg of right triangle would be [tex]x-9[/tex] cm.
We are told that hypotenuse is 9 cm longer than the longer leg.This means that the hypotenuse of right triangle would be [tex]x+9[/tex] cm.
Now, we will use Pythagoras theorem to solve for x as:
[tex]x^2+(x-9)^2=(x+9)^2[/tex]
[tex]x^2+x^2-18x+81=x^2+18x+81[/tex]
Upon simplifying our equation, we will get:
[tex]x^2-18x=18x[/tex]
[tex]x^2-18x-18x=18x-18x[/tex]
[tex]x^2-36x=0[/tex]
[tex]x(x-36)=0[/tex]
Using zero product property, we will get:
[tex]x=0\text{ (or) }(x-36)=0[/tex]
[tex]x=0\text{ (or) }x=36[/tex]
Since longer side of a right triangle cannot be 0, therefore, longer side of the right triangle is 36 cm.
The shorter side of right triangle would be [tex]x-9\Rightarrow 36-9=27[/tex] cm. Therefore, the shorter side of the right triangle would be 27 cm.
The hypotenuse of right triangle would be [tex]x+9\Rightarrow 36+9=45[/tex] cm.Therefore, the hypotenuse of the right triangle would be 45 cm.
