SOLUTION: Please help with this. A box is a cube with edges that measure 2 feet. The sides of the triangle inside the cube are a diagnol of a face, an edge, and a segment with endpoints a

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help with this. A box is a cube with edges that measure 2 feet. The sides of the triangle inside the cube are a diagnol of a face, an edge, and a segment with endpoints a      Log On


   

Question 1050175: Please help with this.
A box is a cube with edges that measure 2 feet. The sides of the triangle inside the cube are a diagnol 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 √2^3. Write the are of the triangle as the number 2 with a rational exponent.
Thank you in advance and please explain how you got the answer and show all work.
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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Please help with this.
A box is a cube with edges that measure 2 feet. The sides of the triangle inside the cube are a diagnol 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 √2^3. Write the are of the triangle as the number 2 with a rational exponent.
Thank you in advance and please explain how you got the answer and show all work.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1.  Make a sketch ! It is necessary !!


2.  One leg is 2 feet long. 
    It is the leg which coincides with the edge of the cube. 
    Is it clear to you?


3.  The second leg  is 2%2Asqrt%282%29 feet long.
    It is the leg which coincides with the diagonal of the face of the cube.
    Is it clear to you?


4.  So, you know the two legs.
    One is 2 feet long, the other is 2%2Asqrt%282%29 feet long.

    Knowing it, you can calculate the area of the triangle.

    It is %281%2F2%29%2A2%2A2%2Asqrt%282%29 = 2^(3/2) square feet.

Solved.