Question

if the perimeter of a right angled triangle is 60 cm and it's hypotenuse is 25cm. find it's area.

Answer 1

Let base of the right angled triangle be b and height be h
Hypotenuse = 25 cm

Perimeter = 60 cm
b + h + 25 = 60
b + h = 60 - 25
b + h = 35 ---(1)

In this triangle,
25² = b² + h²

In equation (1),
Squaring on both sides,
(b+h)² = 35²
b² + h² + 2bh = 1225
25² + 2bh = 1225
2bh = 1225 - 625
2bh = 600
bh = 600/2
bh = 300

Area of the triangle = ½ × b × h
= ½ × 300
= 150 cm²

Answer 2

Let the base ,height of the right angled triangle be x, y.
Given hypotenuse = 25 cm.
By Pythagoras theorem;
x²+y² = 25²
x²+y²=625 .

Given perimeter = 60 cm .
x+y+25= 60
x+y= 35

We have x²+y² = 625

(x+y)²-2xy=625

35² - 625 = 2xy

1225-625 = 2xy

600/2 = xy

300= xy..

Area of the triangle =½*b*h
=½*x*y
=300/2
=150cm²