Question

the sides of a triangle have lengths of x, x+5, and 25. if the longest side is 25, which of the following values of x would make the right triangle?

Answer 1

`x^2+5x-300=0 \\ \\ \Delta =b^2-4ac =5^2 -4*1* (- 300)= 25+1200=1225 \\ \\x_(1)=(-b- √(\Delta ) )/(2a)=(-5- √(1225))/(2 )=(-5-35)/(2)=-(-40)/(2)=-20 \\\\ \ side \ not \ can \ also \ be \ negative`


`x_(2)=(-b+ √(\Delta ) )/(2a)=(-5+ √(1225))/(2 )=(-5+35)/(2)=-(30)/(2)=15\\ \\Ansewr : \ x= 15`