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Semenov [28]
3 years ago
11

The shorter leg of a right triangle is 14 feet less than the other leg. Find the length of the two legs of the hypotenuse is 25

feet.

Mathematics
2 answers:
irakobra [83]3 years ago
6 0

Answer:

  9.233 ft, 23.233 ft

Step-by-step explanation:

If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...

  x^2 + (x +14)^2 = 25^2

  2x^2 +28x +196 = 625

  x^2 +14x = 214.5

  x^2 +14x +49 = 263.5

  (x +7)^2 = 263.5

  x = -7 +√263.5 ≈ 9.23268

The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.

SpyIntel [72]3 years ago
5 0

Answer: 9 ft, 23 ft

Step-by-step explanation:

We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.

(x-14)²+x²=25²

(x²-28x+196)+x²=625

2x²-28x+196=625

2x²-28x-429=0

When we solve for x, we get x=\frac{14+\sqrt{1054} }{2} and x=\frac{14-\sqrt{1054} }{2}.

Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.

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