#34. If AD= 12 and AC= 4y- 36, find the value of y. Then find AC and D.C.

The red segments in the figure tell us that: AD=DC and ED=DB.

AD=DC=12, we also know that AC=AD+DC so AC =12+12=24

AC=4y-36
24=4y-36
4y=24+36=60
y=60/4=30/2=15

Answer: y=15, AC= 24, DC=12

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MrRoyal MrRoyal · Answer 2 · 2021-09-03T21:05:05+02:00

The midpoint of a line is the point that divides the line into two equal halves. Point D divides segment AC into two equal halves.

The value of y is 15
The length of segment AC is 24
The length of segment DC is 12

Given that:

[tex]AD = 12[/tex]

[tex]AC = 4y - 36[/tex]

From the attached figure, point D is the midpoint of line segment AC, So:

[tex]AC = 2 \times AD[/tex]

This gives:

[tex]4y - 36 = 2 \times 12[/tex]

[tex]4y - 36 = 24[/tex]

Collect like terms

[tex]4y = 36 + 24[/tex]

[tex]4y = 60[/tex]

Divide both sides by 4

[tex]y = 15[/tex]

Hence, the value of y is 15

Recall that:

[tex]AC = 4y - 36[/tex]

[tex]AC = 4 \times 15 - 36[/tex]

[tex]AC = 24[/tex]

Hence, the length of AC is 24

Line segment DC has the same value as AD.

Hence, the length of DC is 12