Consider the Pythagorean Theorem and its converse. Which statements are correct? A)
6,8, and 10 are possible side lengths for a right triangle,
8)
10, 15, and 20 are possible side lengths for a right triangle
The Pythagorean Theorem works only for sides of a right triangle
D)
If the sides of a right triangle are of length 8 and 15. its hypotenuse is 17.
E)
The Converse of the Pythagorean Theorem allows us to calculate side
lengths of right triangles.

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step by step resolutions

1) n+n+1+n+2=51

3n+3=51

3n=48

n=16

the three numbers are 16, 17 and 18.

2) x+15=4x

3x=15

x=5

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3) the two digits are x and y.

y=3x

(10x+y)+(10y+x)=88

y=3x

11x+11y=88

y=3x

x+y=8

x+3x=8

x=2

the original number can be either 28 or 82.

4) n+(n+2)+(n+4)=48

3n+6=48

3n=42

n=14

the numbers are 14, 16 and 18.

5) y=x+3

10y+x+10x+y=143

y=x+3

11x+11y=143

y=x+3

x+y=13

x+x+3=13

2x=10

x=5

the original number can be 57 or 75.

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