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Nata [24]
3 years ago
7

What would the answer be

Mathematics
1 answer:
Reil [10]3 years ago
8 0

Answer:

28.28

Step-by-step explanation:

Using Pythagoras' identity on the right triangle

d² = 20² + 20² ← Pythagoras' identity

    = 400 + 400 = 800 ( take the square root of both sides )

d = \sqrt{800} ≈ 28.28 ( to 2 dec. places )


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Step-by-step explanation:

Let c represent the hypotenuse and a and b represent the legs.  Then the Pythagorean Theorem requires that a^2 + b^2 = c^2 = 37^2 = Hypotenuse^2

Also:  a + b + c = Perimeter = 84 units.  

Since c = 37 units, a + b + 37 units = 84 units, or a + b = 47 units, or a = 47 - b.

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Simplifying by combining like terms, we get:  

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Reducing all terms by division by 2, we get:

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The discriminant is therefore b^2 - 4ac, or 529, whose square root is ± 23.

Then the b values of this quadratic in b are

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             2

and then side a has length a = 47 - b = 12  or  35.

Thus, a = 12 and b = 35, and c is given:  37.

Check:  Is 12^2 + 35^2 = 37^2 true?  Is 144 + 1225 = 1369?  YES

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