The perimeter of a right angered triangle is 60cm and it’s area is 120cm^2 . Find the lengths of its sides.
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Answer:
The perimeter of a right angled triangle is 60 cm and its area is 120 cm^2. Find the lengths of its sides. Answer is :10cm, 24 cm and 26 cm.
Step-by-step explanation:
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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