Question

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

Answer 1

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.

Answer 2

Remember to substitute 7 for x to figure out the length of the hypotenuse!