# math

posted by .

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 -

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 -

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

## Similar Questions

1. ### intermediate algebra

A right triangle has two legs and a hypotenuse. One leg of the triangle is 3 feet longer than the other leg. The hypotenuse is 15 feet. Find the length of each leg. I got 12 feet and the other leg is 9 feet Is this correct?
2. ### intermediate algebra

A right triangle has two legs and a hypotenuse. One leg of the triangle is 3 feet longer than the other leg. The hypotenuse is 15 feet. Find the length of each leg. I got 12 feet and the other leg is 9 feet Is this correct?
3. ### Math word problem

The hypotenuse of a right triangle is 22 m long. The length of one leg is 10 m less than the other. Find the lengths of the legs. I have so far let one leg be x the other leg will be x-10 x^2 +(x-10)^2=22^2 x^2+x^2-20x+100=484
4. ### math

I have 14 questions and I was wondering if someone could check my answers. This is a do or die situation. If I don't get an A, I may not get to graduate. I really appreciate you taking your time to double check theses for me. Thanks …
5. ### math

The hypotenuse of a right triangle is 1 cm more than twice the shorter leg, and the longer leg is 9 cm less than three times the shorter leg. Find the lengths of the three sides of the triangle..
6. ### Geometry

I need help in this problem: A 14-foot ladder is leaning against a house so that its top touches the top of the wall. the bottom of the ladder is 8 feet away from the wall. which of these can be used to find the height of the wall?
7. ### Algebra 2 Honors

Hi, I'd like some help with one of the questions on my math homework. It has to do with a right triangle. I'm not sure how to set it up or if I should use the pythagorean theorem. This is the question: Vista county is setting aside …
8. ### math

If the short leg of a 30-60-90 right triangle is 2 feet. What is the long leg and the hypotenuse?
9. ### algebra

Please show solution to this problem. In triangle A, the longer leg is 6 more than the shorter leg and the hypotenuse is 6 more than the longer leg. Find the lengths of each side of this right triangle. Show all calculations. Short …
10. ### algebra

One more triangle question,please. In this triangle,the short leg is x and the longer leg is 1/2x + 11. If the hypotenuse is 2x + 1, what are the lengths of each side of this right triangle?

More Similar Questions