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s344n2d4d5 [400]
3 years ago
14

The length of the hypotenuse of a right triangle is 50 inches. Determine the length of the legs if each leg is the same length.

Mathematics
1 answer:
algol133 years ago
4 0

Answer:

  25√2 ≈ 35.36 inches

Step-by-step explanation:

The Pythagorean theorem can be used to find the leg length for the given conditions. It tells you the relation between legs a, b, and hypotenuse c is ...

  c² = a² +b²

If a=b, and c=50, this becomes ...

  50² = a² +a²

  1250 = a² . . . . divide by 2

  25√2 = a . . . . take the square root

The length of each leg is 25√2 ≈ 35.36 inches.

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Given,
The sum of three integers is 92

So,
Let,
The first integer be "x"
The second integer be "y"
The third integer be "z"

Now,
According to the question,
y = 3x          ..............equation (1)
z = 2x - 10    .............. equation (2)
x + y + z = 92 ..............equation (3)

Now,
Substituting the value of "y" and "z" from equation (1) and (2), we get,

x + (3x) + (2x - 10) = 92
    x + 3x + 2x - 10 = 92
                  6x - 10 = 92
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                           x = 102 / 6
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Now,
substituting the value of "x" in equation (1)
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y = 51

Now,
Substituting the value of "x" in equation (2),

z = 2 (17 ) - 10
z = 34 - 10
z = 24


So, the numbers are 17, 51 and 24


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