# Thread: Math 111 College Algebra-Expressing the area of a right triangle.

1. ## Math 111 College Algebra-Expressing the area of a right triangle.

The vertices of a right triangle in the first quadrant are (0, n), (0,0) and (k, 0).

Draw a picture that represents the situation described.
If the hypotenuse passes trough the point (5,2), express the area of the triangle in terms of k.

Please explain how you got your answer, this is the first time I have encountered a problem like this, and my instructor didn't find it necessary to ask if the class had ever seen this problem before.

Thanks!

2. ## Re: Math 111 College Algebra-Expressing the area of a right triangle.

Here's most of the solution. You should be able to finish.

3. ## Re: Math 111 College Algebra-Expressing the area of a right triangle.

Originally Posted by emilee
The vertices of a right triangle in the first quadrant are (0, n), (0,0) and (k, 0).
Draw a picture that represents the situation described.
If the hypotenuse passes trough the point (5,2), express the area of the triangle in terms of k.
The area of the triangle is $A=.5nk$
Because the points $(0,n),~(5,2),~\&~(k,0)$ are on the same line, then the must determine the same slope.

Thus \begin{align*}\dfrac{n-0}{0-k}&=\dfrac{2-0}{5-k} \\ n&=\dfrac{2k}{k-5} \end{align*}

Now you have a simple substitution.