Expert: Scott A Wilson - 9/13/2009

Question
There are a few questions.
1. Point B is between A and C. If AC=11x-20, AB=3x-8 and BC=6x+4
x=
AC=
AB=
BC=
2. Point R is between S and T. If SR=2x+2, ST=xsquared and RT=7x+8 find x Sr RT and ST



thanks!!

Answer
I will use L() as the length of a line segment.
1. It is nown that L(AC) = 11x-20, L(AB) = 3x-8, and L(BC) = 6x+4.

Since L(AC) = L(AB) + L(BC), we know that 11x-20 = 3x-8 + 6x+4,
which is the same as 11x - 20 = 9x - 4.

Adding 20-9x to both sides gives 2x = 16, or x = 8.
This gives L(AC) = 11x-20 = 88-20 = 68, L(AB) = 3x-8 = 24-8 = 16, and L(BC) = 6x+4 = 52.

Since 68 = 16 + 52, that is the right answer.


2. L(SR) = 2x+2, L(ST) = x², and L(RT) = 7x+18.
Since L(SR) + L(RT) = L(ST), that says that 2x+2 + 7x+8 = x².
That reduces to 0 = x² -9x - 10, which factors to (x-10)(x+1).

We should take x=10, so L(SR) = 2(10)+2 = 22, L(ST) = 10² = 100 and L(RT) = 7(10)+8 = 78.
Now 78 + 22 = 100, so we're good.

We could have taken x=-1, but that would gives us L(SR)=0 and L(RT), L(ST) both being 1.
That does work, but frequently solutions with a 0 length are left out.