# Math Help - Word problem - quadratics

1. ## Word problem - quadratics

The hypotenuse of a right angle triangle is 15 cm. the sum of the legs of the triangle is 21 cm. Find the legs of the triangle.

How do I solve this?

ps I have to solve this using the quadratic formula

2. I would figure that by scaling, you can make $\frac{15}{3}=5$ making the hypotenuse 5, then knowing this, and the 3-4-5 rule, you could make the legs, 3 and 4 respectively, then to convert back to the parameters of the problem, you'd multiply back by 3, giving you $3*3 = 9$ and $4*3 = 12$ which if added, $9+12 = 21$ give you the 21 cm stated in the problem.

3. Originally Posted by dancingqueen9
The hypotenuse of a right angle triangle is 15 cm. the sum of the legs of the triangle is 21 cm. Find the legs of the triangle.

How do I solve this?
Let $a$ and $b$ denote the legs of the right triangle, we know that

$a+b=21$

and

$a^2+b^2=225$

Now solve that system of equations

You should get (its in white so you don't have to see it, if you wish to just highlight below)
x=9 and y=12 or y=9 and x=12...they are describing the same triangle

4. Alright, thanx guys!