Hello,

I'm lost, If the perimeter of triangle XYZ is 12, one side is 5, another side is 4, and the height perpendicular to the third side is 3, what is the triangle's area?

Thank You

The two sides we know are 5 and 4. We know our perimeter is 12, so our third side must be 12-5-4, which is 3.
Thus, our area is this third side times the height times 1/2, which is 3 * 3 * 1/2, which is 4.5

Veritas Help

i was just looking in the questions, and just started the program, so i'm sorry if i'm wrong. But, if the triangle has a perimeter of 12, and we know 1 side is 5 and the other is 4, don't we already now that the third side is 3?- which i see in ur answer...
so if it's 3-4-5: so the area would be 1/2bh or 1/2(3)(4) or 6?
I'm confused why we would use 3 twice in the equation?
thanks for your help

The problem is that we don't know where the height they've given us falls unless they tell us.
Since we don't know whether this is a right triangle, we don't know that two of the actual sides make up the base and height -
IF they had told us that this was a right triangle AND they had told us that the 5 was the hypotenuse, THEN we could have deduced that it was a 3-4-5 triangle and found the third side this way - but we don't have that information.
Rather, we only know that the height and base must be perpendicular to each other. They tell us that "the height perpendicular to the third side is 3" so this is our height, but is NOT a side of the triangle. We use the base of 3 that we found using the perimeter. This is the reason we use two 3's in the calculation of the area.

Make more sense?

Veritas Help

re-read the triangle section and redid the problem without reading your post. made perfect sense. thanks for your answer. i get it now. I appreciate it! i was assuming an incorrect height