Question

Find the value of EB

Answer 1

Answer:

31

Step-by-step explanation:

Given,

AD = 38

EB = 7x - 4

FC = 6x - 6

Now, we have to find the value of X

$eb \: = \frac{1}{2} (ad \: + fc \: )$ ( Mid segment Theorem )

Plug the values

$7x - 4 = \frac{1}{2} (38 + 6x - 6)$

Calculate the difference

$7x - 4 = \frac{1}{2} (32 + 6x)$

Remove the parentheses

$7x - 4 = \frac{32}{2} + \frac{6x}{2}$

$7x - 4 = 16 + 3x$

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

$7x - 3x = 16 + 4$

Collect like terms

$4x = 16 + 4$

Calculate the sum

$4x = 20$

Divide both sides of the equation by 4

$\frac{4x}{4} = \frac{20}{4}$

Calculate

$x = 5$

The value of X is 5

Now, let's find the value of EB

EB = 7x - 4

Plug the value of X

$= 7 \times 5 - 4$

Calculate the product

$= 35 - 4$

Calculate the difference

$= 31$

The value of EB is 31

Hope this helps..

Best regards!!