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The box at the right is a cube with edges that measure 2 feet. The sides of the triangle inside the cube are a diagonal of a face, an edge, and a segment with endpoints at opposite corners of the cube. The triangle is a right triangle with leg lengths 2 and
[tex] \sqrt{ {2}^{3} } [/tex]
. Write the area of the triangle as the number 2 with a rational exponent.​

Respuesta :

MrRoyal

Answer:

[tex]Area = 2 \sqrt{2}[/tex]

Step-by-step explanation:

Given

[tex]Length_1 = 2[/tex]

[tex]Length_2 = \sqrt{2^3}[/tex]

Required

Determine the area of the triangle

The given lengths represent the height and base length of the triangle.

So, the area is;

[tex]Area = \frac{1}{2} * Length_1 * Length_2[/tex]

Substitute values for Length1 and Length2

[tex]Area = \frac{1}{2} * 2 * \sqrt{2^3}[/tex]

[tex]Area = \frac{2}{2} * \sqrt{2^3}[/tex]

[tex]Area = 1* \sqrt{2^3}[/tex]

[tex]Area = \sqrt{2^3}[/tex]

Express 2^3 as 2 * 2 * 2

[tex]Area = \sqrt{2*2*2}[/tex]

[tex]Area = \sqrt{4*2}[/tex]

Split

[tex]Area = \sqrt{4} *\sqrt{2}[/tex]

[tex]Area = 2 *\sqrt{2}[/tex]

[tex]Area = 2 \sqrt{2}[/tex]

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