Q5) Sheetal and Sonika invested money in the business in the ratio 4:5. If the total profit
earned was Rs.27000. Find the share each one should get according to the ratio given
above.
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ANSWER
ABC is a isosceles triangle in which AB=AC
BD Perpendicular to AC
In △ABD
AB
2
=AD
2
+BD
2
...(Pythagoras theoram)
∴AC
2
=AD
2
+BD
2
....(as AB=AC) ...(1)
From diagram, we see that
⇒AC=CD+AD
⇒AC
2
=(CD+AD)
2
From (1) we get,
⇒(CD+AD)
2
=AD
2
+BD
2
CD
2
+AD
2
+2(CD×AD)=AD
2
+BD
2
CD
2
+2(CD×AD)=BD
2
...(AD square gets cancelled from both sides)
BD
2
−CD
2
=2(CD×AD)
Hence proved.
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