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Which of these IS Pythagorean triple?

A) 11,60,61
B) 6,8,15
C) 5,11,12
D) 9,24,25



Which number completes the Pythagorean Triple of 14,48,x?

A) 12
B) 12.5
C) 25
D) 50

User Matter Cat
by
8.9k points

1 Answer

4 votes

If a, b and c are a Pythagorean triple, then:


a^2+b^2=c^2

for a ≤ b < c.

We have:

A) 11, 60, 61

check:


11^2+60^2=121+3600=3721\\\\61^2=3721

CORRECT

B) 6, 8, 15

These are not the sides of the triangle because 6 + 8 = 14 < 15

C) 5, 11, 12

check


5^2+11^2=25+121=146\\\\12^2=144\\\\146\\eq144

INCORRECT

D) 9, 24, 25


9^2+24^2=81+576=657\\\\25^2=625\\\\657\\eq625

INCORRECT

Answer: A) 11, 60, 61

2)

If a, b, c are the sides of the triangle, then:

a + b > c and a + c > b and b + c > a.

We have 14, 48, x. Therefore:

x < 14 + 48

x < 62

and

x + 14 > 48

x > 34

therefore 34 < x < 62

If 34 < x < 48, then:


14^2+x^2=48^2


196+x^2=2304 subtract 196 from both sides


x^2=2108\to x=√(2108)\\\\x=√(4\cdot527)\\\\x=\sqrt4\cdot√(527)\\\\\boxed{x=2√(527)}

If 48 < x < 62, then:


x^2=14^2+48^2


x^2=196+2304


x^2=2500\to x=√(2500)\\\\\boxed{x=50}

Answer: D) 50

User Aardbol
by
7.7k points

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