1.

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

Answer»

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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