The sides of a right triangle are x, x+21, and x+27. what is the length of the hypotenuse
2 answers:
Answer: 51 uinits The three numbers are x , x + 21 and x + 27. The greatest of the 3 numbers is x + 27, so x + 27 has to be the hypotenuse. ---------------------------------------------- Pythagoras Theorem ---------------------------------------------- a² + b² = c² x² + (x+21)² = (x+27)² x² + x² + 42x + 441 = x² + 54x + 729 x² - 12x -288 = 0 (x - 24)(x + 12) = 0 x = 24 or x = -12 (rejected, length cannot be negative) ---------------------------------------------- Find hypotenuse ---------------------------------------------- Hypotenuse = x + 27 = 24 + 27 = 51 units -----------------------------------------------Answer: 51 units ----------------------------------------------
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
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