Relation between Area and Circumference of right triangle

[kalpkhamesra]

For a right angled triangle, the circumference is 24.

A - 24
B- Area of the triangle.

Are A&B equal or the value cannot be determined?

[tommywallach]

I'm going to assume you mean perimeter, rather than circumference. In the future, please make sure you quote questions word for word, rather than from memory. You have no idea how many questions get posted on the forum that we talk about for many posts, only to find out it was written wrong in the first place.

For this question, the important thing to realize is that a triangle with a perimeter of 24 could have a tiny area. Just imagine it has a height of .000000001 and a base of whatever would make all three sides add up to 24. the area would be tiny.

So to work out if the answer is A or D here (because we've already proven the area could be WAY less than 24), we need to think about how we could make the area as large as possible.

Let's think of an EASY triangle with a perimeter of 24, so we don't have to get into crazy radicals. Well, a 3-4-5 triangle has an perimeter of 12, so a 6-8-10 triangle has a perimeter of 24. The area of that triangle is 24.

Thus, the answer is D.