Mixed number: 2 3/4
improper fraction: 11/4
A right triangle's longest side is the hypotenuse
let x=longest, y=middle, and z=shortest
x=y+2
y=2z-1
therefore x=(2z-1)+2=2z+1
find z
z^2+y^2=x^2 by Pythagorean theorem
plug in x and y in terms of z
z^2+(2z-1)^2=(2z+1)^2
z^2+4z^2-4z+1=4z^2+4z+1
subtract the right-hand side's value from the left-hand side's
z^2-8z=0
z(z-8)=0
z=0, 8
z cannot be zero as the sides must have some value to it.
Therefore the shortest side is equal to 8
M
=
0
O
r
m
=
23
15
Explanation:
1
3
m
+
6
m
−
9
3
m
=
3
m
−
3
4
m
⇒
1
+
6
m
−
9
3
m
=
3
m
−
3
4
m
⇒
−
8
+
6
m
3
m
=
3
m
−
3
4
m
⇒
(
−
8
+
6
m
)
×
4
m
=
(
3
m
−
3
)
×
3
m
⇒
−
32
m
+
24
m
2
=
9
m
2
−
9
m
⇒
−
32
m
+
24
m
2
−
9
m
2
+
9
m
=
0
⇒
15
m
2
−
23
m
=
0
⇒
m
(
15
m
−
23
)
=
0
m
=
0
Or
15
m
−
23
=
0
⇒
15
m
=
23
⇒
m
=
23
15
Y=(x-4)/2x-11x+28
y=(x/2x)-(4/2x)-11x+28
y=0.5x-2x-11x-28
1. subtract like terms
2. add 28 on both sides
3. so on and so forth...
