Math, asked by kristina75, 5 months ago

The perimeter of a right angered triangle is 60cm and it’s area is 120cm^2 . Find the lengths of its sides.

Answers

Answered by DeathAura
1

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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