In the triangle solid shown in Figure points A and B are vertices. The triangular faces are isosceles. The solid has a height of 12, a length of 21, and a width of 18. What is the distance between A and B ?

Options

A. `9sqrt(5)`
B. `3sqrt(58)`
C. `3sqrt(74)`
D. `3sqrt(85)`

Answer

C

Explanation

You can find the distance by using the distance formula twice. First, calculate the distance from A to the vertex on the bottom right side of the same face. The vertex distance is 12 (the height), and the horizontal distance is 19, since A is above the midpoint of the edge of the solid.
`D_(1)=sqrt(12^(2)+9^(2))=sqrt(81+144)=sqrt(225)=15`
The distance between A and B is the hypotenuse of the right triangle with sides of length 15 and 21. So you can use the distance formula again.
`D_(21)=sqrt(15^(2)+21^(2))=sqrt(225+441)=sqrt(666)`
`sqrt(666)=3sqrt(74)`