Question

LM is the midsegment of trapezoid ABCD. AB= x + 8, LM = 4x + 3, and DC = 187. What is the value of x?

Answer 1

As LM is drawn from Midpoints of AD and BC, so it is nothing but a Median..

And there is a formula related to Median that is:

\[Length \; LM = \frac{1}{2} \times (AB + CD)\]

Answer 2

Can you do the rest or not??

Answer 3

sorry computer cut off

Answer 4

It is okay..

Can you do now??

Answer 5

im trying to work it out...

Answer 6

is the x multiply or a variable

Answer 7

Okay, take your time..

Let me know if you have doubt..

That is Multiplication..

Answer 8

\[LM = \frac{AB + CD}{2} \]

Answer 9

i dont know if im doing this right, \[4x+3=\frac{ (x+8)+(187) }{ 2 }\]

Answer 10

But I know, you are doing this right..

Answer 11

\[4x+3=\frac{ 275+x }{ 2 }\]

Answer 12

275??

Answer 13

187 + 8 ??

Answer 14

ummm no? ....195.. my bad

Answer 15

Yep, go ahead..

Answer 16

x=64

Answer 17

How??

Answer 18

4x+3=195+x
3x+3=195
3x=192
x=64

Answer 19

Where is 2??

Answer 20

\[4x+3=\frac{ 195+x }{ 2 }\]

Answer 21

2?

Answer 22

Multiply here both the sides by 2..

Answer 23

multiply? doesnt the fraction bar mean divide?

Answer 24

By that you will cancel 2 there..

Answer 25

ok now you lost me

Answer 26

\[2(4x+3)=2(\frac{ 195+x }{ 2 })\]

Answer 27

Have you heard the word "Cross Multiplication" ??

Answer 28

we do that to get rid of 2? and yes i have....

Answer 29

Yep..

To get rid of 2..

Answer 30

ok so now.... it would be...... hold on im workin it out

Answer 31

Now solve this..

Cancel 2 with 2 on Right Hand Side..

Answer 32

Take your time..

Answer 33

is it 8x+6=195+x?

Answer 34

Yep go ahead..

Answer 35

x=27

Answer 36

Nice..

I like this...

Answer 37

thank you for all your help :D

Answer 38

Welcome dear..