Question

The dimensions of a box that is a rectangular prism are 3 inches, 4 inches, and 6 inches. What is the length of the diagonal from the point R to point S, to the nearest tenth of an inch?

Answer 1

7.8 in

Explanation:

Given:-

- The dimension of rectangular prism:

(3 x 4 x 6) inches

Find:-

What is the length of the diagonal from the point R to point S, to the nearest tenth of an inch?

Solution:-

- We will set up an origin with coordinates ( 0 , 0 , 0 ) at point R. Then the coordinates of point S would be ( 3 , 4 , 6 ).

- Then we will use the distance between two points formula in cartesian coordinate system:

Distance =
`√((x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2)`

Where the coordinates of two points ( x1 , y1 , z1 ) & ( x2 , y2 , z2 ).

- Using R( 0 , 0 , 0 ) & S( 3 , 4 , 6 ), the distance |RS| would be:

`|RS| = √((0 - 3)^2 + (0 - 4)^2 + (0 - 6)^2)\\\\|RS| = √( 9 + 16 + 36)\\\\|RS| = √(61) = 7.81024`

- The distance |RS| to nearest 10th of an inch is = 7.8 in