Question

F is the midpoint of AB and E is the midpoint of AC If FE=x+5 and BC=3x+2, What is FE? A)10 B)11 C)12 D)13

Answer 1

Option D is correct.

FE = 13 units

Explanation:

As per the statement: F is the midpoint of AB and E is the midpoint of AC.

If
`FE = x+5 units` and

By midpoint theorem of line states that the points on a line segment equally distant from the two endpoints.

Then, by midpoint theorem of line we have;

`FE =(1)/(2)BC`

Substitute the given values we have;

`x+5 = (1)/(2)(3x+2)`

Multiply both sides by 2 we getl;

`2(x+5) = 3x+2`

Using distributive property:

`a\cdot (b+c) = a\cdot b+ a\cdot c`

2x + 10 = 3x+ 2

Subtract 2 from both sides we get;

2x + 8 = 3x

Subtract 2x from both sides we have;

8 = x

or

x =8 units.

We have to find the value of FE.

FE = x +5 = 8+5 =13 units

Therefore, the value of FE is, 13