Answer:
b = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
a² + b² = c² , that is
12² + b² = (2b)²
144 + b² = 4b² ( subtract b² from both sides )
144 = 3b² ( divide both sides by 3 )
48 = b² ( take square root of both sides )
[tex]\sqrt{48}[/tex] = b , then
b = [tex]\sqrt{16(3)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex]
Using Pythagoras theorem, the length of side [tex]b[/tex] is [tex]4\sqrt{3}[/tex].
The three sides of a right angled triangle is [tex]a, b[/tex], and [tex]c[/tex].
[tex]a=12, c=2b[/tex].
[tex]c[/tex] is the hypotenuse,
Using Pythagoras theorem
So, [tex]c^2=a^2+b^2[/tex]
[tex](2b)^2=(12)^2+b^2[/tex]
[tex]4b^2=144+b^2[/tex]
[tex]4b^2-b^2=144[/tex]
[tex]3b^2=144[/tex]
[tex]b^2=\frac{144}{3}[/tex]
[tex]b^2=48[/tex]
[tex]b=\sqrt{48}[/tex]
[tex]b=4\sqrt{3}[/tex]
So, the length of side [tex]b[/tex] is [tex]4\sqrt{3}[/tex].
Learn more about Pythagoras theorem here:
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