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Reika [66]
2 years ago
5

Solve for x.

Mathematics
1 answer:
Aliun [14]2 years ago
8 0

9514 1404 393

Answer:

  x = 3.6

Step-by-step explanation:

The angle bisector divides the segments proportionally. This means they satisfy ...

  bottom segment / side segment = x/6 = (6-x)/4

Multiplying by 12 gives ...

  2x = 3(6 -x)

  2x = 18 -3x . . . . . eliminate parentheses

  5x = 18 . . . . . . . . add 3x

  x = 3.6 . . . . . . . . . divide by 5

_____

<em>Alternate solution</em>

I like to try to work these mentally. The total of side lengths is 10, so the total base length (6) is 6/10 = 0.6 times that. Then x will be 0.6 times the left side length: 0.6·6 = 3.6 = x.

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so.. simply, use the distance formula, to get their length an add them up, and that's the perimeter of the polygon.


\bf \textit{distance between 2 points}\\ \quad \\&#10;\begin{array}{lllll}&#10;&x_1&y_1&x_2&y_2\\&#10;%  (a,b)&#10;&({{ -1}}\quad ,&{{ 2}})\quad &#10;%  (c,d)&#10;&({{ 2}}\quad ,&{{ 4}})\\&#10;&({{ 2}}\quad ,&{{ 4}})\quad &#10;%  (c,d)&#10;&({{ 3}}\quad ,&{{ -2}})\\&#10;&({{ 3}}\quad ,&{{ -2}})\quad &#10;%  (c,d)&#10;&({{ -2}}\quad ,&{{ -3}})\\&#10;&({{ -2}}\quad ,&{{ -3}})\quad &#10;%  (c,d)&#10;&({{ -1}}\quad ,&{{ 2}})&#10;\end{array}\qquad &#10;%  distance value&#10;d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}

\bf -------------------------------\\\\&#10;d=\sqrt{[2-(-1)]^2+(4-2)^2}\implies d=\sqrt{(2+1)^2+(2)^2}&#10;\\\\\\&#10;d=\sqrt{3^2+2^2}\implies \boxed{d=\sqrt{13}}\\\\&#10;-------------------------------\\\\&#10;d=\sqrt{(3-2)^2+(-2-4)^2}\implies d=\sqrt{1^2+(-6)^2}\implies \boxed{d=\sqrt{37}}\\\\&#10;-------------------------------\\\\&#10;d=\sqrt{(-2-3)^2+[-3-(-2)]^2}\implies d=\sqrt{(-5)^2+(-3+2)^2}&#10;\\\\\\&#10;d=\sqrt{(-5)^2+(-1)^2}\implies \boxed{d=\sqrt{26}}

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so, those are their lengths, sum them all up, that's the polygon's perimeter.

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