The sides of a right triangle are x, x+21, and x+27. what is the length of the hypotenuse

Hypotonuse is the longest side

pythagorean theorem tells us that if the lengths of the legs of a right triangle are a and b and the hyptonuse is c then

we can see that x+27 is bigger than the other 2 numbers so x+27 must be the length of the hyptonuse

therefor

expand

add like terms

subtract from both sides

solve, use quadratic formula
for ,
so for , a=1, b=-12, c=-288
subsituting


x=-12 or 24
x can't be negative since we can't have a negative side ength

x=24

x+27 is hypotonuse
x+27=24+27=51

the hypotonuse is 51 units long