A certain right triangle with integer side lengths has perimeter 160. What is its area?

Guest Apr 25, 2022

#1**+1 **

Use the formula A = (a)(b)/2 to find its area, but you haven't given me the sides of the triangle and only the perimeter so I can only guess what the length of each side is.

Griff Apr 26, 2022

#2**0 **

*A certain right triangle with integer side lengths has perimeter 160. What is its area?*

It's a right triangle, Its sides are integers. So the sides must be a Pythagorean Triple.

No Pythagorean Triple totals 160 per https://en.wikipedia.org/wiki/Pythagorean_Triple

So this triangle doesn't exist.

_{.}

Guest Apr 26, 2022

#3**+1 **

Actually, it does exist.

The triple can also be a multiple of a primitive Pythagorean Theorem.

For example, the triple \((8, 15, 17)\) has a perimeter of 40. We can scale this up by 4, to have the triple \((32, 60,68)\).

The bases of this triangle are 32 and 60, so the area is: \(\Large {32 \times 60 \over 2} = \text{____}\)

BuilderBoi Apr 26, 2022