Question

In the diagram below of △QUT, R is a point on QT and S is a point on QU such that RS II TU, QS=x−3, RT=20, QR=16, and QU=2x+2. Find the length of QS.

Answer 1

QS=32 units

Step-by-step explanation:

In QUT,

QS=$x - 3$

QU=$2x + 2$

QR=$16$

RT=$20$

QT= QR + QT =

$20 + 16 = 36$

$by \: basic \: proportionality \: theorem$

QS/QU=QR/QT

$\frac{x - 3}{2x - 2} = \frac{16}{36} \\ 36(x - 3) = 16(2x + 2) \\ 36x - 108 = 32x + 32 \\36x - 32x = 108 + 32 \\ 4x = 140 \\ x = 35$

QS= x - 3 = 35 - 3 = 32units

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