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

Make a drawing...


/|
/ |
/ |
/ |
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:

10^2 = (x+2)^2 + x^2

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