One of the basic question from similarity chapter in which we have been asked to find the length of sides PY and XY by using the properties of similarities
ML Aggarwal Avichal Publication, Similarity, class 10, chapterv13ii, question no 1c
Rajan@2021Guru
In the figure (iii) given below, if XY∥ QR,PX=1 cm,QX=3 cm,YR=4.5 cm and QR=9 cm, find PY and XY.
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From the figure,
XY∥QR,PX=1cm,QX=3 cm, YR=4.5 cm and QR=9 cm,
So, PX/QX=PY/YR
1/3=PY/4.5
By cross multiplication we get,
(4.5×1)/3=PY
PY=45/30
PY=1.5
Then, ∠X=∠Q
∠Y=∠R
So, ∠PXY∼△PQR
Therefore, XY/QR=PX/PQ
XY/9=1/(1+3)
XY/9=1/4
XY=9/4
XY=2.25.