The larger leg of a right triangle is 2 feet longer than its smaller leg. The hypotenuse is 4 feet longer than the smaller leg. How many feet long is the larger leg?

We are given a right triangle whose legs we name as x, x+2 and x+4. The Pythagorean theorem states that the square of the hypotenuse's length is equal to sum of the squares of its legs. hence, we apply this to the given dа ta:

a2 + b2 = c2

We substitute the given data

x2 + (x+2) 2 = (x+4) 2

We expound the given squares

x2 + x2 + 4x + 4 = x2 + 8x + 16

We group next the like terms

2x2-x2 = 8x - 4x + 16 - 4

x2 = 4x + 12

(x2-4x-12) = 0

we factor the given quadratic equation

(x-6) * (x+2) = 0

x1 = 6

x2 = - 2

The valid solution set would be 6 since there are no negative measurements, so the answer to this problem would be 6+2 = 8 units.