Question

Calculate de perimeter... Pleaseee

Answer 1

assuming the triangle is an isosceles, or namely that the two slanted sides are equal to each other, and thus the line in the middle is perpendicular to the base, so we can just use the pythagorean theorem to get the length of the slanted sides and then add them together with the base for the perimeter, Check the picture below.

$\sqrt{(12xy^2)^2+\left( \cfrac{7x+3}{2}\right)^2}\implies \sqrt{(12xy^2)^2+ \cfrac{(7x+3)^2}{2^2}} \\\\\\ \sqrt{12^2x^2y^4+ \cfrac{49x^2+42x+9}{4}}\implies \sqrt{ \cfrac{4\cdot 12^2x^2y^4+49x^2+42x+9}{4}} \\\\\\ \cfrac{\sqrt{576x^2y^4+49x^2+42x+9}}{\sqrt{4}}\implies \cfrac{\sqrt{576x^2y^4+49x^2+42x+9}}{2}$

so that'd be the length of one of the a slanted sides, we have two of them equal, so let's just add them up and the base.

$\cfrac{\sqrt{576x^2y^4+49x^2+42x+9}}{2}+\cfrac{\sqrt{576x^2y^4+49x^2+42x+9}}{2}+(7x+3) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{\large perimeter}}{7x+3+\sqrt{576x^2y^4+49x^2+42x+9}}~\hfill$