Question

Given a right triangle whose side lengths are all integer multiples of 8, how many units are in the smallest possible perimeter of such a triangle?

Answer 1

96 units.

Explanation:

Let a, b represent legs and c represent hypotenuse of the given right triangle.

We are told that in the given triangle all side lengths are all integer multiples of 8. Using Pythagoras theorem, we can represent this information in an equation as:

`(8a)^2+(8b)^2=(8c)^2`

`64a^2+64b^2=64c^2`

Upon dividing both sides by by 64, we will get:

`a^2+b^2=c^2`

We know that smallest Pythagoras triplet is such that
`a=3, b=4\text{ and }c=5`.

Since all sides are multiple of 8, so the smallest possible perimeter would be
`8(3+4+5)=8*12=96`.

Therefore, the smallest possible perimeter of such a triangle would be 96 units.