Question

the sides of an acute triangle are x, 35, and 37 where x is the shortest side find the range of possible values for x and express it as an inequality

ok so i did
x^2+35^2>37^2
x^2+1225>1369
-1225> -1225
x^2> 144
then i took the square root of both and i got x= 12 but i dont know what to do about the ranges

Answer 1

it's acute, so you don't want to use pythagoras
rather, you need to know that for a triangle to exist, the sum of two of it's sides must be greater than the third

Answer 2

so you get 35 + 37 > x
x+35 > 37
x+ 37 > 35
solve to find your ranges

Answer 3

so all of the work that i did i should erase? and do it the other way

Answer 4

yeahhhhh

Answer 5

sorry about that :/

Answer 6

no problem :)
in the problem it says x is the shortest side tho

Answer 7

ok but ^ those inequalities still hold true
you can add that x < 35

Answer 8

but what about 37 ? would i do x< 35+37?

Answer 9

im sorry it takes some time for me to catch on

Answer 10

because the sum of two sides must be greater than the third side
of course that's moot here, x<35 overtakes x< 35+37, but that doesn't make it not a requirement
get it?

Answer 11

it's like, if someone said bill is taller than 4 feet, and then someone else said, actually, bill is taller than 5 feet, that doesn't make the first person wrong.

Answer 12

:( still alittle confused i get what your saying but still little confused

Answer 13

http://www.mathwarehouse.com/geometry/triangles/triangle-inequality-theorem-rule-explained.php
so now this is your triangle, ok?

according to the triangle inequality theorem, the inequalities i first posted are true
because x is the shortest side, it must be shorter than the two sides you have listed. 35 is the shorter of the two, so x < 35. that's where the last one comes from