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.............Answer
If triangle BNV ~ triangle BRG, BR=4x+7 and BG= 18 find the value of x
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The parallel sides AB, PQ, and CD, gives similar triangles, ∆ABD ~ ∆PQD and ∆CDB ~ ∆PQB, from which we have;
From the given information, we have;
- ∆ABD ~ ∆PQD
- ∆CDB ~ ∆PQB
According to the ratio of corresponding sides of similar triangles, we have;
Which gives;
QD × x = BD × z
BD × z = (1 - QD/BD) × y = y - (QD × y/BD)
Therefore;
BD × z = y - (QD × y/BD)
BQ × y = y - (QD × y/BD)
BQ × y = y - (z × y/x) = y × (1 - z/x)
(1 - z/x) = BQ
BD × z = y × (1 - z/x)
BD = (y × (1 - z/x))/z
Therefore;
QD × x = y × (1 - z/x)
(BD-BQ) × x = y × (1 - z/x)
(BD-(1 - z/x)) × x = y × (1 - z/x)
BD = (y × (1 - z/x))/x + (1 - z/x)
BQ + QD = (1 - z/x) + (y × (1 - z/x))/x
BD = BQ + QD
(y × (1 - z/x))/x + (1 - z/x) = (y × (1 - z/x))/z
(1 - z/x)×(y/x + 1) =(1 - z/x) × y/z
Dividing both sides by (1 - z/x) gives;
y/x + 1 = y/z
Dividing all through by y gives;
(y/x + 1)/y = (y/z)/y
- 1/x + 1/y = 1/z
Therefore;
Learn more about characteristics similar triangles here:
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