The answer is: "
x = ." ;
AND: "
y = ."
_______________________________________________________Explanation:
______________________________________________________The sides of a "45-45-90" (right triangle) are: "a", "a" ; and "a√2" .
Note that: "a√2" is the hypotenuse length— and the other 2 (TWO) sides of the triangle are of equal length— {since: "a = a" .}.
_______________________________________________________As such: "x = y" ; and the hypotenuse, "x√2", equals:
"
" .
__________________________________________________Note: The Pythagorean theorem (for the side lengths of right triangles):
→ " a² + b² = c² ;
in which: "c = the hypotenuse length" ;
"a = one of the other side lengths"
"b = the remaining side length" .
____________________________________________________Note that: "x = y" ;
so: " x² + x² = 2x " ;
2x² = x√2 ;
2x² = c² ; in which "c" is the hypotenuse; Solve for "x" and "y" ; Since "x = y" ; solve for "x" ;
2x² = c² ;
→ Given (from image attached); " c =
" .
→ c² = (
)² ;
=
;
=
;
=
;
=
;
____________________________________________________ → 2x² =
Divide each side of the equation by "2" ;
2x² / 2 =
) ÷ 2 ;
x² =
;
Note: The "32" cancels out to "16"; and the "2" cancels out to "1" ;
→ {since: "32 ÷ 2 = 16" ; and since: "2 ÷ 2 = 1 " } l
And we have;
x² =
;
→ Multiply by "
" ; to eliminate the "√3" in the "denominator" ;
→
*
;
=
÷
;
= "
" .
_____________________________________________________The answer is: "
x = ." ;
AND: "
y = ."
_____________________________________________________
Does "x√2" = the hypotenuse length shown?
that is: Does "x√2" = "
" ?
Note: " x =
" ; (from our calculated answer) .
_____________________________________________________
→
Multiply this value by "√2" ; and see if we get the same values as the given hypotenuse:
→
* √2 ;
=
?? ;
→ Note: "√3 * √2 = √(3 * 2) = √6 " ;
_________________________________________
→
;
= ;
→ which is the value of the hypotenuse shown in the figure!
Yes; the answer does make sense!
_________________________________________________