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

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

- math -
**MathGuru**, Tuesday, May 1, 2012 at 5:55pm
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.

- math -
**MathGuru**, Tuesday, May 1, 2012 at 5:58pm
Remember to substitute 7 for x to figure out the length of the hypotenuse!

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