Two right triangle of base 15 cm and height 20 cms were joined together along their hypotenuse. Find its perimeter and area.
Answers
Answer:
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Step-by-step explanation:
Let ABC be the right angled triangle such that AB=15cm and AC=20cm
Using Pythagoras theorem we have
⇒BC
2
=AB
2
+AC
2
⇒BC
2
=15
2
+20
2
⇒BC
2
=225+400=625
⇒BC=25cm
Let OB=x and OA=y
Applying pythagoras theorem in triangles OAB and OAC we have
AB
2
=OB
2
+OA
2
;AC
2
=OA
2
+OC
2
⇒15
2
=x
2
+y
2
;20
2
=y
2
+(25−x)
2
⇒x
2
+y
2
=225;(25−x)
2
+y
2
=400
{(25−x)
2
+y
2
}−{x
2
+y
2
}=400−225
⇒(25−x)
2
−x
2
=175⇒x=9
Putting x=9 in x
2
+y
2
=225 we get
81+y
2
=225⇒y
2
=144⇒y=12
Thus we have OA=12cm and OB=9cm
Volume of the double cone = volume of cone CAA' + volume of cone BAA'
=
3
1
π×(OA)
2
×OC+
3
1
π×(OA)
2
×OB=
3
1
π×12
2
×16+
3
1
π×12
2
×9
=
3
1
×3.14×144×253768cm
3
Surface area of the double cone = curved surface area of cone CAA
′
+ curved surface area of cone BAA
′
=π×OA×AC+π×OA×AB
=(π×12×20+π×12×15)cm
2
=420πcm
2
=420×π=420×3.14
=1318.8cm
2