Respuesta :
Answer: [tex]24, 32, 40\ in.[/tex]
Step-by-step explanation:
Given
The shorter side is 8 inches shorter than the long side.
The hypotenuse is 8 inches longer than the long side.
Suppose the length of the long side is x
Short side is [tex]x-8[/tex]
hypotenuse is [tex]x+8[/tex]
using Pythagoras theorem
[tex]\Rightarrow \left( x-8\right)^2+\left( x\right)^2=\left( x+8\right)^2\\\Rightarrow x^2+64-16x+x^2=x^2+64+16x\\\Rightarrow x^2-32x=0\\\Rightarrow x\left( x-32\right)=0\\\Rightarrow x=0\ \text{or}\ 32[/tex]
Neglecting 0 as length cannot be zero
Shorter side is [tex]32-8=24\ in.[/tex]
long side [tex]x=32\ in.[/tex]
hypotenuse [tex]32+8=40\ in.[/tex]
