Question

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


`\sqrt{ {2}^(3) }`
. Write the area of the triangle as the number 2 with a rational exponent.​

Answer 1

`Area = 2 √(2)`

Explanation:

Given

`Length_1 = 2`

`Length_2 = √(2^3)`

Required

Determine the area of the triangle

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

So, the area is;

`Area = (1)/(2) * Length_1 * Length_2`

Substitute values for Length1 and Length2

`Area = (1)/(2) * 2 * √(2^3)`

`Area = (2)/(2) * √(2^3)`

`Area = 1* √(2^3)`

`Area = √(2^3)`

Express 2^3 as 2 * 2 * 2

`Area = √(2*2*2)`

`Area = √(4*2)`

Split

`Area = √(4) *√(2)`

`Area = 2 *√(2)`

`Area = 2 √(2)`