Aright triangle's hypotenuse is 10 inches long. the length of one leg of a right triangle is 2 inches more than the second leg. what are the lengths of the legs of the triangle?

  8 inches and 6 inches

Step-by-step explanation:

The hypotenuse length of 10 is 2 times 5, so there is a possibility that the triangle is a 3-4-5 triangle scaled by a factor of 2. The leg length difference of 2 confirms this. The right triangle of interest has sides of 6 inches, 8 inches, and 10 inches, double the sides of a 3-4-5 triangle.

Since "one leg" is 2 inches longer, it must be the 8-inch leg. The "second leg" must be the 6-inch leg.

The 3-4-5 right triangle shows up in many algebra and geometry problems, so is useful to remember.

If you want to solve this algebraically, you can assign x as the length of "one leg" and (x -2) as the length of "the second leg." Then the Pythagorean theorem tells you ...

  10² = x² +(x -2)²

  100 = 2x² -4x +4

  x² -2x -48 = 0 . . . . . subtract 100, divide by 2

  (x -8)(x +6) = 0 . . . . .factor

  x = 8 . . . . . . . . . . . . . the positive solution; the only one of interest

One leg is 8 inches; the second leg is 6 inches.

3; 9 is 8 to -4

step-by-step explanation: