If BC = 2x + 1, CD = 3x - 4 and BD = 22, find the value of x. b. Using the value of x, find BC and CD
2x+1=3x-4=22. Solve for x. Put x back in to each part (2x+1 and 3x-4) for each segment.
To find the value of x, we can use the fact that the sum of the lengths of segments BC and CD must be equal to the length of segment BD.
So, we can set up the equation: BC + CD = BD
Substituting the given values, we get: (2x + 1) + (3x - 4) = 22
Combining like terms, we have: 5x - 3 = 22
Next, we isolate the x term by adding 3 to both sides of the equation: 5x = 25
Finally, dividing both sides by 5 gives us: x = 5
Now that we have found the value of x, we can substitute it back into the expressions for BC and CD to find their respective lengths.
BC = 2x + 1
Substituting x = 5, we get: BC = 2(5) + 1 = 10 + 1 = 11
CD = 3x - 4
Substituting x = 5, we get: CD = 3(5) - 4 = 15 - 4 = 11
Therefore, the value of x is 5, BC is 11, and CD is 11.