Answer:
4[tex]\sqrt{13}[/tex]
4[tex]\sqrt{13}[/tex] + 8
4[tex]\sqrt{13}[/tex] + 16
Step-by-step explanation:
as per the given information:
shorter leg = x
longer leg = x + 8
hypotonuse = x + 8 + 8
remember the Pythagorean theorem, which states
x^2 + y^2 = n^2
where x and y are the legs and n is the hypotenuse
so now one can set up an equation:
x^2 + ( x + 8 )^2 = ( x + 16 ) ^2
simplify and solve using inverse operations:
first preform the square
x^2 + x^2 + 16x + 64 = x^2 + 32x + 256
then preform inverse opertations and simplify
2x^2 + 16x + 64 = x^2 + 32x + 256
-x^2 -x^2
x^2 + 16x + 64 = 32x + 256
-16x -16x
x^2 + 64 = 16x + 256
- 64 -64
x^2 = 16x + 192
-16x -16x
x^2 - 16 = 192
x^2 -4^2 = 192
remember the differnt ways of writing a special square
(x - 4) (x + 4) = 192
x = 4[tex]\sqrt{13}[/tex]
now add 8 to find the longer leg
4[tex]\sqrt{13}[/tex] + 8
an add another 8 to find the hypotenuse
4[tex]\sqrt{13}[/tex] + 8 + 8
4[tex]\sqrt{13}[/tex] + 16
