The base of the triangle is roughly 8.90 cm and the height is roughly 0.45 cm.
Explanation:
The formula for the area of a triangle is given by:
[tex]A=\frac{bh}{2} \\ \\ \\ b:base \\ \\ h:height[/tex]
We know that the base of a triangle is 8 more than twice its height, so:
[tex]b=2h+8[/tex]
And the area of the triangle is:
[tex]A=2cm^2[/tex]
So matching all this information we have:
[tex]2=\frac{(2h+8)h}{2} \\ \\ 4=(2h+8)h \\ \\ 2h^2+8h-4=0[/tex]
Using quadratic formula:
[tex]2h^2+8h-4=0 \\ \\ \\ a=2 \\ \\ b=8 \\ \\ c=-4 \\ \\ \\ h_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ h_{12}=\frac{-8 \pm \sqrt{8^2-4(2)(-4)}}{2(2)} \\ \\ h_{12}=\frac{-8\pm \sqrt{96}}{4} \\ \\ h_{1}=\frac{-8-4\sqrt{6}}{4}=-2-\sqrt{6} \\ \\ \\ h_{2}=\frac{-8+4\sqrt{6}}{4}=-2+\sqrt{6}[/tex]
But h can't be negative, so our unique solution is:
[tex]h=-2+\sqrt{6}[/tex]
For the base:
[tex]b=2h+8 \\ \\ b=2(-2+\sqrt{6})+8 \\ \\ b=-4+2\sqrt{6}+8 \\ \\ b=4+2\sqrt{6}[/tex]
So the base of the triangle is roughly 8.90 cm and the height is roughly 0.45 cm.
Learn more:
Volume of a box: https://brainly.com/question/10501080
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