Posted by Jess on Monday, April 30, 2012 at 10:43pm.
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!
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