A right triangle has side lengths of x-1, x+1, and x+3. What is its perimeter?

If you’re really on your right triangles game, you might instantly think of the Pythagorean triples you know and see if any fit into that scheme (hint: one will!). If not, just put those values into the Pythagorean theorem and solve for x:

(x-1)^2 + (x+1)^2=(x+3)^2

(x^2 -2x + 1) + (x^2+2x+1)=x^2+6x+9




x=7 \text{ or }x=-1

From there, you know x = 7, because the sides of the triangle aren’t going to be negative.

That means your sides are 6, 8, and 10, and your perimeter is 24.

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