One leg of right triangle is 2cm more than the other the hypotenuse is10cm find the measure of the two legs

Make a drawing...

Code:

---

      /|
      / |
    /  |
    /  |
10 /    | x+2
  /    |
 /      |
/_______|
    x

---

Let's call the shorter length x and the longer one x+2, while the hypotenuse is 10.

Using Pythagoras' Theorem, we know that:



Can you solve this quadratic now? :)

Let x be the first leg
x + 2 is the second
hyp² = 10² = (x² + (x+2)²)
100 = x² + x² + 4x + 4
2x² + 4x – 96 = 0
x² + 2x – 48 = 0
factor
(x – 6)(x + 8) = 0
x = 6, –8
skipping the negative answer, we have
x = 6

checking
leg 1 = 6
leg 2 = 8
h = √(6² + 8²)
OK

b