The length of one leg of a right triangle is 8ft.The length of hypotenuse is 4 ft longer than the other leg.What are the lengths of hypotenuse and...

Use the Pythagorean Theorem:  a^2 + b^2 = c^2, where a and
b are the length of the legs and c is the
hypotenuse.

Substitute 8 in for
a.

8^2 + b^2 = c^2

You are
given that the hypotenuse is 4 ft longer than the other leg, therefore c = b + 4. 
Substitute b + 4 in for c.

64 + b^2 = (b +
4)^2

Use FOIL to expand.

64 +
b^2 = b^2 + 8b + 16

Subtract b^2 from both
sides.

64 = 8b + 16.

Subtract
16 from both sides.

48 =
8b

Divide both sides by 8.

6 =
b

c = b + 4 = 6 + 4 =
10

length of other leg = 6
ft

length of hypotenuse = 10
ft