| (i) What is the distance between the parks through town? |
| (ii) What is the distance from Park A to Park B through point R? |
A) i-9 m ii-13m
B) i-8 m ii-12.5 m
C) i-8.75 m ii-12 m
D) i-9m ii-14m
Correct Answer: C
Solution :
(i) Since,\[CD||AB\] [Given] In \[\Delta RCD\] and \[\Delta RBA,\] we have \[\angle BAR=\angle RDC\] \[\angle ABR=\angle RCD\] [Alternate interior angles] \[\therefore \] \[\Delta RCD\tilde{\ }\Delta RBA\] [By AA similarity] \[\Rightarrow \] \[\frac{BR}{RC}=\frac{AB}{CD}\] ...(i) \[\Rightarrow \] \[\frac{7.5}{1.2}=\frac{AB}{1.4}\Rightarrow AB=\frac{7.5\times 1.4}{1.2}=8.75m\] i.e., Distance between the parks through town is\[8.75\text{ }m\]. (ii) In right \[\Delta CRD,\]we have \[{{(CD)}^{2}}={{(CR)}^{2}}+{{(RD)}^{2}}\] \[\Rightarrow \] \[R{{D}^{2}}={{(1.4)}^{2}}-{{(1.2)}^{2}}=0.52\Rightarrow RD=0.72m\] Since \[\Delta RCD\tilde{\ }\Delta RBA\] \[\therefore \] \[\frac{BR}{RC}=\frac{AR}{RD}\,\,\Rightarrow \,\frac{7.5}{1.2}=\frac{AR}{0.72}\] \[\Rightarrow \] \[AR=\frac{7.5\times 0.72}{1.2}=4.5m\] i.e., Distance from Park A to Park B through point \[R=AR+RB=4.5\,m+7.5m=12\,m\]
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