Question

If b is the midpoint of ac, ac=cd, ab=3x+4, ac=11x-17, and ce=49, find de

Answer 1

Answer:

de=11

Step-by-step explanation:

We are given that b is the midpoint of ac

ac=cd, ab=3x+4,ac=11x-17 and ce=49

We have to find the value of de

b is the midpoint of ac therefore we have

ab=bc

ac=ab+bc=ab+ab=2ab

$11x-17=2(3x+4)$

$11x-17=6x+8$

$11x-6x=8+17=25$

$5x=25$

$x=\frac{25}{5}=5$

Then , substitute the value of x

$ab=3(5)+4=19$

ac=$11(5)-17=55-17=38=cd$

ce=cd+de

49=38+de

$de=49-38$

de=11

Answer 2

First, we draw our line.

 

|------------------------------------------------------------------------------------|

a                                                                                                            e

 

 

Next, break up this line into segments using the information.

 

|----------------------|----------------------|--------------------|------------------|

a                            b                            c                         d                      e

 

 

The entire line is 29.

 

ab + bc + cd + de = ae

ab + bc + cd + de = 29

 

You also know that

 

bd = bc + cd

 

 

Due to midpoint theorem,

 

ab = bc

cd = de

 

 

Then,

 

2ab + 2cd = 29

 

 

The equations we will use are

 

bd = bc + cd                       eq1

2bc + 2cd = 29                   eq2

 

 

Dividing both sides of the equation in eq2 yields

 

bc + cd = 14.5

 

bd = bc + cd

bd = 14.5