What is the value of x? Enter your answer in the box. units A triangle B D R is given with a midsgement of Q C where Q is between B and D and C is between R and D. B Q is 24 units long. Q D is 40 units long. R C is 18 units long. C D is labeled x. Segment B R is parallel to segment Q C.
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Answer:
30
Step-by-step explanation:
Hi,
Given triangle BDR and QC a mid segment where Q is on BD and C is on DR
such that BR || QC,
Given BQ = 24 units
QD = 40 units
RC = 18 units
CD = x,
BD = BQ + QD = 24 + 40 = 64 units
DR = DC + CR = x + 18,
Now consider triangle BDR and QDC,
∠QDC = ∠BDR (same angle)
∠DCQ = ∠DRB (since BR || QC)
∠CQD = ∠RBD(since BR || QC).
Hence , both the triangle are similar,
Thus their sides should be proportional i.e.,
DQ / BD = CD/DR
⇒40/64 = x/x + 18
⇒5/8 = x/x + 18
⇒5x + 90 = 8x
⇒3x = 90
⇒x = 30
Hope, it helped !
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