A certain right triangle with integer side lengths has perimeter 160. What is its area?
+8 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.
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.
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+2666 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: \(\Large {32 \times 60 \over 2} = \text{____}\)
