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In a triangle, the longest side is 6x2 + 8 and the base is 12x -3. If the shortest side is half of the length of the longest side, what is the perimeter of the triangle? Must be written in standard form

Verified Answer :

apologiabiology

longest is 6x^2+8
half of that is 3x^2+4


perimiter=sum of sides


so
6x^2+8+12x-3+3x^2+4=
9x^2+12+9

boffeemadrid

The perimeter of the triangle is required.

The perimeter of the triangle is given by the equation \(P=9x^2+12x+9\)

Longest side = \(6x^2+8\)

Base = \(12x-3\)

Shortest side = \(\dfrac{6x^2+8}{2}\)

Perimeter is given by

\(P=6x^2+8+12x-3+\dfrac{6x^2+8}{2}=6x^2+12x+5+\dfrac{6x^2+8}{2}\\\Rightarrow P=\dfrac{12x^2+24x+10+6x^2+8}{2}\\\Rightarrow P=\dfrac{18x^2+24x+18}{2}\\\Rightarrow P=9x^2+12x+9\)

The perimeter of the triangle is given by the equation \(P=9x^2+12x+9\)

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