Question

the perimeter of a right angle triangle is 60cm and its hypotenuse is 25cm find the area of the triangle​

Answer 1

Answer:

150 cm is the correct answer

Answer 2

150cm

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

${ab}^{2} + {bc}^{2} = {ac }^{2} \:$

+BC

2

(35-x)*2+x*2=(25)*2

⇒2x*2 −70x+600=0(÷2)

⇒x*2 −35x+300=0

⇒x*2−20x−15x+300=0

⇒(x−20)(x−15)=0

⇒x=20 or x=15

If x=20, then AB=35−x=15 and BC=x=20

Area = (BC×AB)÷2

=(20×15)÷2

=300÷2

=150cm

If x=15, then AB=35−x=20 and BC=x=15

Area = (BC×AB)÷2

=(20×15)

=300÷2

=150cm