What is the value of x?
Triangle B D R with line segment Q C parallel to segment B R with C between R and D and Q between B and D. B Q equals 26, Q D equals 39. R C equals 18. C D equals x.
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Answer:
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Answer: The value of x is 81.
To solve for the value of x, we can use the fact that segment QC is parallel to segment BR. This means that triangle BQC and triangle BDR are similar triangles. We can use this similarity to set up a proportion:
BQ/QC = BD/DR
Substituting the given values, we get:
26/(QC) = BD/DR
We also know that QC + RC = CD, so we can substitute RC = 18 and QC = CD - RC = x - 18:
26/(x - 18) = BD/DR
We can simplify this by cross-multiplying:
26DR = BD(x - 18)
We can also use the fact that BQ + QD = BD to substitute for BD:
26DR = (BQ + QD)(x - 18)
26DR = (26 + 39)(x - 18)
26DR = 65(x - 18)
Now we need to find DR, the length of segment DR. To do this, we can use the fact that triangle BDR is a right triangle with BD as the hypotenuse. We can use the Pythagorean theorem to find the length of BD:
BD^2 = BR^2 + DR^2
We know that segment QC is parallel to segment BR, so we can use the fact that triangles BQC and DRC are similar to set up another proportion:
BQ/QC = DR/RC
Substituting the given values, we get:
26/(x - 18) = DR/18
Simplifying, we get:
DR = 18(26/(x - 18))
Now we can substitute this value for DR in the equation we derived earlier:
26DR = 65(x - 18)
26(18)(26/(x - 18)) = 65(x - 18)
Simplifying, we get:
2028/(x - 18) = 65
Cross-multiplying, we get:
2028 = 65(x - 18)
Solving for x, we get:
x = 81
Therefore, CD equals 81.
Learn more about the Pythagorean theorem here
https://brainly.in/question/2829237
Learn more about proportion here
https://brainly.in/question/48326727
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