Question

the lengths of the side of a right triangle are x, x+3, and x+6. What is the length if the hypotenuse of this triangle

Answer 1

x^2+(x+3)^2=(x+6)^2
x=9
hypotenuse is the longest so 9+6=15

Answer 2

x x+3 x+6 x^2 (x+3)^2 (x+6)^2 c^2-a^2-b^2=0
1 4 7 1 16 49 32
2 5 8 4 25 64 35
3 6 9 9 36 81 36
4 7 10 16 49 100 35
5 8 11 25 64 121 32
6 9 12 36 81 144 27
7 10 13 49 100 169 20
8 11 14 64 121 196 11
9 12 15 81 144 225 0
10 13 16 100 169 256 -13
11 14 17 121 196 289 -28
12 15 18 144 225 324 -45
13 16 19 169 256 361 -64
14 17 20 196 289 400 -85
15 18 21 225 324 441 -108
16 19 22 256 361 484 -133
17 20 23 289 400 529 -160

Answer 3

Plug your sides into the Pythagorean Theorem and then simplify and solve for x

\[a^2+b^2=c^2\]

Let a=x,b=x+3, and c=x+6 since x+6 has to be the longest side
Therefore we will have \[x^2+x^2+6x+9=x^2+12x+36\]
So now we simplify to get
\[2x^2+6x+9=x^2+12x+36\]
then move terms to set equation to 0
\[x^2-6x-27=0\]
factor to get
(x-9)(x+3)=0
x={-3,9}
Since x is the length of one of the sides it cannot be negative so we can discard -3 as a solution, therefore we set our hypotenuse to be c=x+6
so c=9+6=15

Answer 4

sashley0915 answer is correct given x+6 is the hyp