Studdy AI Logo
Math

QuestionIf BC=6xBC=6x, CD=9CD=9, and BD=9xBD=9x, find the value of BCBC. Simplify your answer as a fraction, mixed number, or integer.

Studdy Solution

STEP 1

Assumptions1. BC =6x. CD =93. BD =9x4. BD = BC + CD (Based on the segment addition postulate, which states that if B is between A and C, then AB + BC = AC)

STEP 2

We can set up an equation based on the segment addition postulate.
BD=BC+CDBD = BC + CD

STEP 3

Now, plug in the given values for BD, BC, and CD to set up the equation.
9x=6x+99x =6x +9

STEP 4

To solve for x, we need to isolate x on one side of the equation. We can do this by subtracting6x from both sides of the equation.
9x−6x=6x−6x+99x -6x =6x -6x +9

STEP 5

implify the equation.
3x=93x =9

STEP 6

Now, divide both sides of the equation by3 to solve for x.
3x3=93\frac{3x}{3} = \frac{9}{3}

STEP 7

implify to find the value of x.
x=3x =3

STEP 8

Now that we have the value of x, we can substitute it into the equation for BC to find the value of BC.
BC=6xBC =6x

STEP 9

Substitute x =3 into the equation.
BC=6×3BC =6 \times3

STEP 10

Calculate the value of BC.
BC=18BC =18So, BC equals18.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord