Given:In ΔRST ,PQ is a line parallel to RS and also dividing RT and ST in same ratio(by basic proportionality theorem)
simple Proportionality theorem says that if a heat is drawn parallel to one side of a triangle to intersect the various other two side in distinctive points, the various other two sides are split in the exact same ratio.
Therefore, the length of QT is 65 cm.
You are watching: In the figure pq is parallel to rs the length of rp is 2 cm
The size of SQ is 7 cm.
Since we have given that
Length the RP = 6cm
Length the PT = 18 cm
Length the QT = 21 cm
We need to uncover the length of SQ.
Since PQ is parallel come RS.
So, their proportion would be very same anyhow.
So, that becomes,
Hence, the size of SQ is 7 cm.
PT = 30 cm
RP = 5 cm
RT = RP + PT = 35 cm
TQ = 60 cm
See figure attached
It is evident that angles
30/PQ = 35/RS
30/35 = PQ/RS
PQ/RS = 0.857
60/PQ = (60 + QS)/RS
60/(60 + QS) = PQ/RS
60/(60 + QS) = 0.857
60 = 0.857*(60 + QS)
60 - 0.857*60 = 0.857*QS
QS = (60 - 0.857*60)/0.857
QS = 10
A. 22 cm
By the Thales organize we recognize that: If we have two parallel directly lines and also they reduced other two ones, for example lines that a triangle climate they develop proportional segments, i beg your pardon means:
RP is proportional come PT and also SQ is proportional come QT, we have the right to express the as:
And we have:
RP is 8 cm
PT is 16 cm
SQ is 11 cm
We need to calculate QT:
QT= (16*11)/8 =22cm
by looking at the figure, we can determinate the the distance sq is 6cm, given that:
pq and also rs space parallel.
the street pr is 5cm.
the angle s watch minor that angle r.
for this reasons, the others alternatives are really unlikely to it is in correct.
we recognize that
In the figure
The triangle PTQ and also RTS are comparable by AA Similarity Theorem
If two number are similar, climate the proportion of its matching sides is equal
substitute the values and solve for ST
substitute the worth of ST in the equation A to uncover the worth of SQ
Option C 10 cm
we know that
If two triangles are similar, climate the ratio of its equivalent sides is proportional
In this problem
Triangles PTQ and RTS are similar
Solve for SQ
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