Answer: a = 8; b = 15; c = 17
Step-by-step explanation:
c = b + 2 and c = 2a + 1
b = c − 2 and a = [tex]\frac{c-1}{2}[/tex]
c² = b² + a²
[tex]c^{2} = (c-2)^{2} + \frac{c-1}{2}\\[/tex]
[tex]c^{2}= \frac{4 (c-2)^{2}+(c - 1)^{2} }{4}[/tex]
[tex]4c^{2}={4 (c^{2} + 4 -4c)+c ^{2} + 1-2c[/tex]
[tex]4c^{2}={4 c^{2} + 16 -16c)+c ^{2} + 1-2c[/tex]
[tex]c^{2}-18c+17=0[/tex]
[tex]c(c -17)-1(c-17)=0[/tex]
[tex](c -1)(c-17)=0[/tex]
c = 1 or c = 17
If c = 1 then b = 1 - 2 = -1, that's not possible
So x = 17
b = 17 - 2 = 15
a = [tex]\frac{17-1}{2} = 8[/tex]
Length sides of the triangle are 17 cm, 15 cm and 8 cm.
I saw some of this on a site but I want to make sure its correct so we're gonna apply the pythagorean theory and see if its correct.
[tex]a^{2} + b^{2} = c^{2} \\8^{2} + 15^{2} = 17^{2} \\64 + 225 = 289\\289 = 289\\[/tex]
This shows that this is correct.
Hope this helped! Again, some of this was from a site, not from me.
