The perimeter of right angle triangle is 60 CM its hypotenuse is 25 cm find the area of the triangle

The perimeter of right angle triangle is 60 CM its hypotenuse is 25 cm

1.	The perimeter of right angle triangle is 60 CM its hypotenuse is 25 cm find the area of the triangle
Answer» Here,\xa0a + b + c = 60, c = 25a + b = 6 0 - ca + b = 6 0 - 2 5 = 35Using Pythagoras theorem\|{tex}a ^ { 2 } + b ^ { 2 } = 625{/tex}\xa0Using identity\xa0{tex}( a + b ) ^ { 2 } = a ^ { 2 } + b ^ { 2 } + 2 a b{/tex}\xa0{tex}35 ^ { 2 } = 625 + 2 a b{/tex}\xa01225 - 625 = 2abor, ab = 300Hence, Area of\xa0{tex}\\triangle A B C = \\frac { 1 } { 2 } a b = 150 \\mathrm { cm } ^ { 2 }{/tex}