Question

4. EF is the median of trapezoid ABCD.

B
X +12
с
E
4x-18
F
3x-4
A
Part I: Solve for x. Show your work. (4 points)

Answer 1

x = 11

BC = 23

AD = 29

EF = 26

Explanation:

Given:

Trapezoid ABCD, having,

median = EF = 4x - 18

base BC = x + 12

base AD = 3x - 4

Required:

Part I: value of x

Part II: Length of BC, AD, and EF.

Solution:

Part I: Value of X

The median length of a trapezoid is said to be the ½ of the sum of the 2 bases of the trapezoid.

Therefore, EF = ½(BC + AD)

4x - 18 = ½((x + 12) + (3x - 4)

4x - 18 = ½(x + 12 + 3x - 4)

4x - 18 = ½(x + 3x +12 - 4)

4x - 18 = ½(4x + 8)

Multiply 2 by both sides

2(4x - 18) = 4x + 8

8x - 36 = 4x + 8

Add 36 to both sides

8x - 36 + 36 = 4x + 8 + 36

8x = 4x + 44

Subtract 4x from both sides

8x - 4x = 4x + 44 - 4x

4x = 44

Divide both sides by 4

x = 11

Part II:

BC = x + 12 = 11 + 12 = 23

AD = 3x - 4 = 3(11) - 4 = 33 - 4 = 29

EF = 4x - 18 = 4(11) - 18 = 44 - 18 = 26