The lenght of one leg of a right triangle is 4 ft.The length of the hypotenuseis 2 feet longer than the other leg. Find the length of the hypotenuse and the other leg.
The length of the hypotenuse is ___ft.
The length of the otherleg is___ft.
Let the other leg=L, then the hypotenuse is:
L +2. Now, we use Pythogoras' theorem:
(L + 2)^2=L^2 + 4^2
Solve for L:
(L+2)^2 = L^2+16
Subtract L^2+16 from both sides:
-16-L^2+(L+2)^2 = 0
Expand out terms of the left hand side:
4 L-12 = 0
Factor constant terms from the left hand side:
4 (L-3) = 0
Divide both sides by 4:
L-3 = 0
Add 3 to both sides:
Answer: L = 3 feet Hypotenuse=3+2=5 feet
| L = 3
