Question

Complete statement WZ=? and RS=? in the figure shown.

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asked 2021-08-11
To Complete: the statement WZ=? and RS=? in the figure shown.
Given:
Figure is shown below.
image
RW=15, ZR=10 and ZS=8

Answers (1)

2021-08-12
Calculation:
In \(\displaystyle\triangle{R}{W}{Z}\ {\quad\text{and}\quad}\ \triangle{Z}{W}{S}\).
\(\displaystyle\angle{W}{R}{Z}\stackrel{\sim}{=}\angle{W}{Z}{S}\therefore\) (Given)
\(\displaystyle\angle{W}\stackrel{\sim}{=}\angle{W}\therefore\) (Common)
\(\displaystyle{W}{Z}\stackrel{\sim}{=}{W}{Z}\therefore\) (Common)
By AAS similarity, \(\displaystyle\triangle{R}{W}{Z}\sim\triangle{Z}{W}{S}\).
Therefore,
\(\displaystyle{\frac{{{R}{W}}}{{{Z}{W}}}}={\frac{{{Z}{R}}}{{{S}{Z}}}}={\frac{{{W}{Z}}}{{{W}{S}}}}\)
\(\displaystyle{\frac{{{15}}}{{{Z}{W}}}}={\frac{{{10}}}{{{8}}}}\)
\(\displaystyle{Z}{W}={\frac{{{15}\times{8}}}{{{10}}}}\)
ZW=12
\(\displaystyle{\frac{{{Z}{R}}}{{{S}{Z}}}}={\frac{{{W}{Z}}}{{{W}{S}}}}\)
\(\displaystyle{\frac{{{10}}}{{{8}}}}={\frac{{{12}}}{{{W}{S}}}}\)
\(\displaystyle{W}{S}={\frac{{{12}\times{8}}}{{{10}}}}\)
WS=9.6
And
RS=RW-SW
RS=15-9.6
RS=5.4
Therefore, the answer is 12 and 5.4.
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