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17

The median segment (HJ = 5x+2) has a length that is the average of the lengths of the other parallel segments, (KL = 4x+1, and NM = 27). Writing this relation as an equation, we have ...

... 5x + 2 = (4x + 1 + 27)/2

... 10x + 4 = 4x + 28 . . . . . . multiply by 2, collect terms

... 6x = 24 . . . . . . . . . . . . . . add -4x-4

... x = 4 . . . . . . . . . . . . . . . . . divide by 6

Then the length of KL is ...

... KL = 4x +1

... = 4·4 +1 = 17

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: