The lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20. This can be obtained by adding um and md which is equal to ud. An equation is obtained and solve for x.
<h3>What is the required lengths ?</h3>
Given that, um=5x+30
md=3x+80
ud=10x+20
We know that m is the midpoint of ud
Thus, um + md = ud
5x+30 + 3x+80 = 10x+20
5x+3x + 30+80 = 10x+20
8x + 110 = 10x+20 (taking terms with x to one side of equation)
10x - 8x = 110 - 20
2x = 90
⇒ x = 45
Therefore the lengths,
um=5x+30 = 5(45)+30 = 225 + 30 = 255
md=3x+80 = 3(45)+80 = 135 + 80 = 215
ud=10x+20 = 10(45)+20 = 450 + 20 = 470
Hence the lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20.
Learn more about collinear points here:
brainly.com/question/5191807
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