Question

Find the length of the median and the missing base. Be sure to show all your work. NO LINKS!!!​

Answer 1

YZ = 12, ML = 11

Explanation:

The median is half the sum of the parallel bases, that is

YZ =
`(KN+LM)/(2)`

4x - 16 =
`(13+2x-3)/(2)` ( multiply both sides by 2 to clear the fraction )

8x - 32 = 10 + 2x ( subtract 2x from both sides )

6x - 32 = 10 ( add 32 to both sides )

6x = 42 ( divide both sides by 6 )

x = 7

Then

YZ = 4x - 16 = 4(7) - 16 = 28 - 16 = 12

ML = 2x - 3 = 2(7) - 3 = 14 - 3 = 11

Answer 2

The bottom is 11

The median is 12

Explanation:

The median is the average of the top and bottom

(13+ 2x-3) /2 = 4x-16

Combine like terms

(10+2x)/2 = 4x-16

Divide by 2

5+x = 4x-16

Subtract x from each side

5+x-x = 4x-16-x

5 = 3x-16

Add 16 to each side

5+16 = 3x-16+16

21 = 3x

Divide by 3

21/3 = 3x/3

7 =x

The bottom is 2x-3 = 2*7-3 = 14-3 = 11

The median is 4x-16 = 4*7-16 = 28 -16 = 12