math
posted by Jess on .
the hypotenuse of a right triangle is 3 less than 4 times the shortest leg. if the longest leg is 24cm, how long is the hypotenuse

Some basics:
24 = longest leg
x = shortest leg
4x  3 = hypotenuse
Remember the following:
a^2 + b^2 = c^2
24^2 + x^2 = (4x  3)^2
576 + x^2 = 16x^2  24x + 9
Set the equation equal to 0:
0 = 15x^2  24x  567
Factoring:
0 = 3(5x^2  8x  189)
0 = 3(5x + 27)(x  7)
Set the factors equal to 0:
5x + 27 = 0; x = 27/5
x  7 = 0; x = 7
Since you can't have a negative number, x = 7 is your only answer.
I hope this explanation will help with other problems of this type. 
Remember to substitute 7 for x to figure out the length of the hypotenuse!