Question

the perimeter of right triangle is 144 cm and its hypotenuse measures 65 cm find the length of other two sides and calculate its area verify the result by using heron's formula

Answer 1

65+a+b=144 a+b=79. a^2+b^2=65^2=4225. From these two equations 2ab=79^2-4225=2016. ab=1008. From this eqn and a+b=79. we get the quadratic a^2-79a+1008=0. whose solution is a=63 or. 16 obv b=16. a=63. or vice versa. Area=0.5*63*16=504
From heron area=sart(72*7*9*56)=504 ok