Question

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

Answer 1

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