Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

There is a right triangle. The hypotenuse is 17 units. The sum of the other two sides is 23. Find the length of the two other sides.

Thanks for everyone's help in advance!

share|cite|improve this question
up vote 0 down vote accepted

$a+b=23 \implies b=23-a$.

Note that $a^{2}+b^{2}=17^{2}$ and that $a+b=23$.

Substituting $b=23-a$ in $a^{2}+b^{2}=17^{2}$ gets you:

$a^{2}+(a-23)^{2}=289 \implies 2a^{2}-46a+240=0$

Then apply the quadratic formula:

$a=\frac{46 \pm \sqrt {46^{2}-(4)(2)(240)}}{(2)(2)} =$ $\frac{46 \pm \sqrt {46^{2}-(1920)}}{(4)}\implies$$ a=15$ or $a=8$. Then you plug the a value into the first equation and you get that one of the sides is 15 units and the other side is 8 units.

share|cite|improve this answer

Well, we know that $$a+b=23 \qquad\text{and}\qquad a^2+b^2=17^2=289.$$ Substituting $b=23-a$ into the second equation will give you a quadratic equation in $a$. It's quite likely that of the two solutions to that quadratic equation, only one will be positive. There's your value of $a$, and then $b=23-a$ recovers $b$.

share|cite|improve this answer

From the Pythagorean theorem, you have $a^2+b^2=c^2$ with $c=17, a+b=23$. This is three equations in three unknowns.

share|cite|improve this answer

There are only a few sets of small integers that form right triangles. These are: $$(3,4,5)\\ (5,12,13)\\ (7,24,25)\\ (8,15,17) $$

and multiples of these, for example $2\cdot(3,4,5) = (6,8,10)$. You should memorize these, because teachers like to use them over and over again.

In this case the problem mentions that the hypotenuse is 17, so you should immediately ask if this is the $(8,15,17)$ triangle. Since $8+15=23$, it is and you have the answer and can go on to the next problem faster than the person at the next desk.

share|cite|improve this answer
+1 for something other than the obvious – bubba May 22 '13 at 4:11

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.