Question

Please help with math homework!

Answer 1

Answer:

x = 5

Step-by-step explanation:

To do this, you need to use the Thales theorem.

You can actually apply this theorem and choose two sides of the figure to do it.

In this case, I will choose segment LM and MN and look for a ratio with DE and EF like this:

LM/MN = DE/EF

This theorem states that you can stablish a ratio between two segments assuming that you have at least two paralels lines, like DL || EM || FN

Therefore, it's time to replace the values of those segments and solve for X:

LM/MN = DE/EF

14/16 = 6x -9 / 4x + 4

7/8 = 6x - 9 / 4x + 4

7(4x+4) = 8(6x-9)

28x + 28 = 48x - 72

72 + 28 = 48x - 28x

100 = 20x

x = 100/20

x = 5