Question

Perimeter of a right angle triangle is 60 cm.If it's area is 150 cm2 ,what is it's hypotenuse?

Answer 1

Answer:

25 cm.

Step-by-step explanation:

Consider a right angled triangle with sides as a cm , b cm and c cm.

Perimeter of right angled triangle = a+b+c = 60 cm

Area of right triangle = 1/2(ab) = 150 cm²

Also by Pythagoras theorem we know that a² + b² = c²

Now

ab = 300  (given as area)

a+ b + c = 60

=> a+b = 60-c  

squaring on both sides

=> (a+b)² = (60 - c)²

=> a²+ b² + 2ab = 3600 + c² - 120c

By Pythagoras theorem we know that a² + b² = c²; Also ab = 300

=> c²+ 2 * 300 = 3600 + c² - 120c

=> 120c = 3600 - 600 = 3000

=> c = 3000/120 = 25 cm.

Thus hypotenuse = 25 cm.