Question 287323
1. 

Let first leg = x
second leg = x+2

Use Pythag. Theorem: {{{a^2+b^2=c^2}}}

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

Expand the (x+2)^2 term:

{{{x^2 + x^2 +4x +4=10^2}}}
{{{2x^2+4x-96=0}}}
{{{2(x^2+2x-48)=0}}}

Factor, by finding two numbers that multiply to -48 and add up to 2.

{{{2(x+8)(x-6)=0}}}
x=-8, or x=6

The side of a triangle can't be a negative number, so the answer must be x=6.

That means the second leg is equal to x+2=6+2=8 feet.

Leg 1 = 6 feet, Leg 2 = 8 feet, Hypotenuse = 10 feet.

Question 2)

Let x = the other leg
Hypotenuse = x+1

Use Pythag. Theorem: {{{c^2=a^2+b^2}}}

{{{(x+1)^2 = 5^2 + x^2}}}

Expand the left side:

{{{x^2 + 2x + 1 = 25 + x^2}}}
{{{2x+1=25}}}
{{{2x=24}}}
{{{x=12}}}

So the other leg is 12 units, and the hypotenuse is 13 units.