Question

A)
What value of
x
that is less than 65 will make the set
a Pythagorean triple?
(1 point) (x, 56, 65)
x
=
85.8
x
=
1
,
089
x
=
9
x
=
33
A)
Given that
is a Pythagorean triple, what is the value of
x
?
(1 point) (x, 12, 2x + 3)
x
=
5
x
=
9
x
=
13
x
=
25

Answer 1

1) (x, 56, 65): x^2 + 56^2 = 65^2 → x^2 = 65^2 − 56^2 = (65−56)(65+56) = 9·121 = 1089 → x = 33.

2) (x, 12, 2x+3): x^2 + 12^2 = (2x+3)^2 → x^2 +144 = 4x^2 +12x +9 → 0 = 3x^2 +12x −135 → x^2 +4x −45 =0 → (x+9)(x−5)=0 → x = 5 (positive side length).