Question

If the perimetre of a right angled triangle is 60 cm and it's hypotenus is 25 cm , then find its area.

Answer 1

Let a, b, c be base, height and hypotenuse respectively.

You have c=25 and a+b=35

and a2+b2=c2=252a2+b2=c2=252.

Here the area of triangle is 12ab12ab.

Then (a+b)2=352(a+b)2=352

⇒2ab=352−(a2+b2)⇒2ab=352−(a2+b2)

⇒2ab=4(30)(5)⇒2ab=4(30)(5)

⇒12ab=150⇒12ab=150.

Hence area of triangle is 150 sq. units