Question

the perimeter of right triangle is 60cm it's hypotenuse is 25cm find area of triangle​

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Perimeter of triangle

= 60 cm

Also,

Length of hypotenuse

= 25 cm

Assume

Other sides = x and y

${\boxed{\sf\:{Pythagoras\;Theorem}}}$

(Hypotenuse)² = (base)² + (height)²

(25)² = x² + y²

Also

Perimeter of triangle = 60 (Given)

x + y + Hypotenuse = 60

x + y + 25 = 60

x + y = 60 - 25

x + y = 35 cm

Now

${\boxed{\sf\:{Squarring\;Both\;sides}}}$

(x + y)² = (35)²

x² + y² + 2xy = 1225 cm²

Hence,

(25)² + 2xy = 1225

625 + 2xy = 1225

2xy = 1225 - 625

2xy = 600

xy = 300 cm²

Now,

$\tt{\rightarrow\dfrac{1}{2}xy=\dfrac{1}{2}\times 300}$

$\tt{\rightarrow\dfrac{1}{2}xy=150}$

Therefore,

Area of this triangle

= 150 cm²

So,

$\Large{\boxed{\sf\:{Area\;of\;triangle = 150 cm^2}}}$