SOLUTION: Hi! I had a question about the Pythagorean Theorem. One of the legs of a right triangle is 15 inches long and the sum of the other leg and the hypotenuse equals 25 inches. Determin

Algebra ->  Pythagorean-theorem -> SOLUTION: Hi! I had a question about the Pythagorean Theorem. One of the legs of a right triangle is 15 inches long and the sum of the other leg and the hypotenuse equals 25 inches. Determin      Log On


   

Question 967208: Hi! I had a question about the Pythagorean Theorem. One of the legs of a right triangle is 15 inches long and the sum of the other leg and the hypotenuse equals 25 inches. Determine the length of the hypotenuse and the unknown leg?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let x be length of other side, h be length of hypotenuse
x + h = 25
15^2 + x^2 = h^2
we have two equations in two unknowns
solve first equation for x and substitute for x in second equation
15^2 + (25-h)^2 = h^2
225 + 625 -50h +h^2 = h^2
subtract h^2 from both sides of =
850 -50h = 0
add 50h to both sides of =
50h = 850
h = 17, therefore
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hypotenuse is 17 inches and the other leg is 25-17 = 8 inches
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to check answer substitute in second equation
15^2 + 8^2 = 17^2
225 + 64 = 289
289 = 289
our answer checks