i am thinking of a right triangle, whose sides can be represented by x - 5, 2x, and 2x + 1. find the lengths of the three sides

Answer 1

(2x+1)^2 = (2x)^2 + (x-5)^2

4x^2 +4x + 1 = 4x^2 +x^2 -10x +25

x^2 -14x +24 = 0

(x-12)(x-2) = 0

x = 2, 12

hypotenuse =2(12)+1 = 25

smallest side = 12-5 = 7

3rd side =2(12) = 24

ignore x=2 as it involves a negative length for the smallest side

the three sides are 7, 24 and 25

check the answer

25^2 = 7^2 +24^2

625 = 49 + 576