95.2k views
5 votes
Point C is on line segment bar (BD). Given BC=x+4,CD=5x, and BD=5x+7, determine the numerical length of bar (CD).

User Weky
by
8.5k points

1 Answer

0 votes

Final answer:

To find the numerical length of CD when point C is on line segment BD, we express BD as the sum of BC and CD. By setting up and solving the equation x + 4 + 5x = 5x + 7, we determine x to be 7 and thus, the numerical length of CD is 35 units.

Step-by-step explanation:

Since point C is on line segment BD, we can express BD as the sum of BC and CD. The problem states that BC equals x + 4, CD equals 5x, and BD equals 5x + 7. To find the numerical length of CD, we can set up the equation x + 4 + 5x = 5x + 7 since BD is the sum of BC and CD.

Solving for x, we get:

Combine like terms on each side: x + 5x = 5x and 4 = 7

This simplifies to 6x = 5x + 7

Subtract 5x from both sides: x = 7

Now that we have the value for x, we can find the numerical length of CD by substituting x into 5x:

CD = 5(7)

CD = 35

Therefore, the numerical length of CD is 35 units.

User Stephen Lloyd
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.