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

 Apr 25, 2022
 #1
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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.

 Apr 26, 2022
 #2
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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. 

.

 Apr 26, 2022
 #3
avatar+1370 
+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: \(\Large {32 \times 60 \over 2} = \text{____}\)

 Apr 26, 2022

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