Math, asked by Mister360, 6 hours ago

The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle.

Answers

Answered by CopyThat
12

Step-by-step explanation:

Given :

Perimeter of a right angled triangle is 60cm.

Its hypotenuse is 25cm.

To find :

Area of the triangle.

Solution :

Let ABC be the right angled triangle, where BC = x cm.

Perimeter of triangle = Sum of all the sides of a triangle

  • AB + BC + CA = 60 cm
  • AB + x + CA = 60 cm
  • AB + x = 60 - 25
  • AB + x = 35
  • AB = 35 - x

Using Pythagoras theorem,

  • AB² + BC² = AC²

⇒ (35 - x)² + (x)² = 25²

⇒ 2x² - 70x + 625 = 0

⇒ 2x² - 40x - 30x + 625 = 0

⇒ 2x(x - 20) -30(x - 20) = 0

⇒ (x - 20)(2x - 30)=0

x = 20 or 15

If x = 20 cm,

  • AB = 35 - 20
  • AB = 15 cm

Area of triangle,

⇒ 1/2 × base × height

  • 1/2 × BC × AB
  • 1/2 × 20 × 15
  • 150 cm²

If x = 15 cm,

  • AB = 35 - 15
  • AB = 20 cm

Area of triangle,

⇒ 1/2 × base × height

  • 1/2 × BC × AB
  • 1/2 × 15 × 20
  • 150 cm²

∴ Area of the triangle is 150 cm².

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Attachments:
Answered by rajatraj929
0

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

Step-by-step explanation:

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