Perimeter of a right angle triangle is 60cm and sum of the squares of sides is 1250sq.cm. Find the length of the hypotenuse and th

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1. Answer:

   Let ABC be the given right angled triangle such that base=BC=x cm and hypotenuse AC=25cm

   Now, perimeter =60cm

   AB+BC+AC=60

   AB+x+25=60

   AB=35−x

   By Pythagoras theorem, we have

   AB

   2

   +BC

   2

   =AC

   2

   ⇒(35−x)

   2

   +x

   2

   =25

   2

   ⇒2x

   2

   −70x+600=0

   ⇒x

   2

   −35x+300=0⇒x

   2

   −20x−15x+300=0⇒(x−20)(x−15)=0⇒x=20orx=15

   If x=20, then AB=35−x=15 and BC=x=20

   Area =

   2

   1

   (BC×AB)=

   2

   1

   (20×15)=150cm

   2

   If x=15, then AB=35−x=20 and BC=x=15

   Area =

   2

   1

   (BC×AB)=

   2

   1

   (15×20)=150cm

   2

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