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QT = x + 6, SR = 12, PS = 27 and TR = x - 4. Find QT.

User NLR
by
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1 Answer

3 votes

we know that

The side splitter theorem states that if a line is parallel to a side of a triangle and the line intersects the other two sides, then this line divides those two sides proportionally

so

In this problem

SR/SP=RT/TQ

substitute the given values

12/27=(x-4)/(x+6)

solve for x

12(x+6)=27(x-4)

12x+72=27x-108

27x-12x=72+108

15x=180

x=12

Find QT

QT=x+6

QT=12+6=18

therefore

the answer is

QT=18

User Tarun Sharma
by
8.8k points

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