Question

Find the perimeter of a right triangle whose area is 24 in^2 given that one leg is two inches shorter then the other leg

Answer 1

please mark it as a brainliest answer so perimeter =8+6+10=24

Answer 2

Hey


Let the one leg be x


Then ,


another leg be ( x - 2 )


Now ,


Area given = 24 cm²



Area = 1 / 2 * base * height ( legs )


=> 1 / 2 * x * ( x - 2 ) = 24

=> x ( x - 2 ) = 48


=> x² - 2x - 48 = 0


D = ( - 2 ) ² - 4 ( - 48 )


= 4 + 192

= 196

So,

√D = √ 196


= 14 .


Now ,

x = - b + √D / 2a


x = 2 + 14 / 2


x = 16 /2

x = 8


So ,

one leg = 8 cm


second leg = 6 cm


now,

hypotenuse = √ ( 8 ) ² + ( 6 ) ²


= √ 64 + 36


= √ 100


= 10 cm


So ,

perimeter = sum of all sides


= ( 6 + 8 + 10 ) cm

= 24 cm



thanks :)

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