Question

Perimeter of a 19h mangle is 60 cm its hypotence is 25cm Find the area of the teriangle.​

Answer 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+BC²=AC²

⇒(35−x)² +x²=25²

⇒2x²−70x+600=0

⇒x²−35x+300=0⇒x²−20x−15x+300=0⇒(x−20)(x−15)=0⇒x=20orx=15

If x=20, then AB=35−x=15 and BC=x=20

Area = 1/2

(BC×AB)=1/2

(20×15)=150cm²

If x=15, then AB=35−x=20 and BC=x=15

Area = 1/2

(BC×AB)= 1/2

(15×20)=150cm²