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⏺ Let ABC be a triangle with <C =90° , Draw CD perpendicular to AB. Choose points M and N on sides AC and BC respectively such that DM is parallel to BC and DN is parallel to AC. If DM =5 , DN =4 , Then AC and BC are respectively equal to :-
a) 41/4 , 41/5
b) 39/4 , 39/5
c) 38/4 ,38/5
d) 37/4 , 37/5
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Answer:
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Answered by
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Answer:
Step-by-step explanation:
MDNC forms a square.
CN=MD=5
MC=DN=4
Let ND be x.
For ΔCDN,
By pythagorus theorem,
CD
2
=4
2
+5
2
CD=
41
For \Delta DNB,
By pythagorus theorem,
DB=
4
2
+x
2
For \Delta CDB,
By pythagorus theorem,
CB
2
=CD
2
+DB
2
(CN+NB)
2
=41+(16+x
2
)
(5+x)
2
=41+16+x
2
25+10x+x
2
=53+x
2
x=
5
16
CB=5+x=5+
5
16
CB=
5
41
Similarly,
Take AM y.
In \Delta AMD,
AD=25+y
2
In \Delta ACD,
(4+y)
2
=(25+y
2
)+41
y=
4
25
AC=
4
25
+4
AC=
4
41
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