Question

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

Answer 1

Answer:

Area of the triangle is 150cm^2.

Step-by-step explanation:

Given,

Perimeter of the triangle( right-angled triangle ) is 60 cm. And, length of its hypotenuse is 25 cm.

Let the other sides be a and b.

Pythagoras Theorem :

• Hypotenuse^2 = base^2 + height^2
• ( 25 cm )^2 = a^2 + b^2 { here }

= > Perimeter of triangle = 60 cm

= > a + b + hypotenuse = 60 cm

= > a + b + 25 cm = 60 cm

= > a + b = 60 cm - 25 cm

= > a + b = 35 cm

= > ( a + b )^2 = ( 35 cm )^2 { square on both sides }

= > a^2 + b^2 + 2ab = 1225 cm^2

= > ( 25 cm )^2 + 2ab = 1225 cm^2 { from above, a^2 + b^2 = ( 25 cm )^2 }

= > 625 cm^2 + 2ab = 1225 cm^2

= > 2ab = 1225 - 625 cm^2

= > 2ab = 600 cm^2

= > ab = 300 cm^2

= > 1 / 2 ab = 1 / 2 x 300 cm^2

= > 1 / 2 ab = 150 cm^2 { half of product of its sides represents its area }

= > Area of this triangle = 150 cm^2

Hence, area of the triangle is 150cm^2.