The leght of one leg of a right triangle is 8 ft. The legth of the hypotenuse is 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 other leg is ___ft.
Let U=be the unknown side, the we have the hypotenuse:
U + 2. Now we use Pythogoras' theorem:
(U + 2)^2=U^2 + 8^2
U^2+4U+U=U^2+64,
Solve for U:
(U+2)^2 = U^2+64
Subtract U^2+64 from both sides:
-64-U^2+(U+2)^2 = 0
Expand out terms of the left hand side:
4 U-60 = 0
Factor constant terms from the left hand side:
4 (U-15) = 0
Divide both sides by 4:
U-15 = 0
Add 15 to both sides:
Answer: | U = 15 feet Hypotenuse=15+2=17feet
Let U=be the unknown side, the we have the hypotenuse:
U + 2. Now we use Pythogoras' theorem:
(U + 2)^2=U^2 + 8^2
U^2+4U+U=U^2+64,
Solve for U:
(U+2)^2 = U^2+64
Subtract U^2+64 from both sides:
-64-U^2+(U+2)^2 = 0
Expand out terms of the left hand side:
4 U-60 = 0
Factor constant terms from the left hand side:
4 (U-15) = 0
Divide both sides by 4:
U-15 = 0
Add 15 to both sides:
Answer: | U = 15 feet Hypotenuse=15+2=17feet
