Question

A triangular pyramid has an equaliteral triangle, RDO, as its base andisosceles triangles as its sides. HDC is a 45°-45°-90° triangle. If C is thecentroid of RDO and M is the midpoint of Ro, find MC.

Answer 1

Pink Friday, this is the solution:

As we reviewed before, these are the steps to find out the solution:

Step 1: Calculate the length of the legs of the isosceles right triangle HDC

Hypotenuse = 12√3

Leg 1 = x

Leg 2 = x

Using the Pythagorean Theorem, we have:

(12√3)² = x² + x²

144 * 3 = 2x²

432 = 2x²

Dividing by 2 at both sides:

432/2 = 2x²/2

216 = x²

Square root at both sides:

√216 = √x²

14.7 = x

In consequence,

• HC = 14.7 m = 6√6 m

,

• CD = 14.7 m = 6√6 m

Step 2: Now we calculate the centroid of triangle RDO, as follows:

This is an equilateral triangle, therefore:

RD = DO = RO

Let's recall that the centroid is always located in the interior of the triangle. The centroid is located 2/3 of the distance from the vertex along the segment that connects the vertex to the midpoint of the opposite side.

Thus, if CD = 14.7, then

MC = 6√6/2

MC = 3√6 or 7.35m or 7.4 m (rounding to the next tenth)