An equilateral triangular lamina has each side equal to 50cm. How far is the centre of gravity from each vertex?
the centre of gravity is located at the intersection of the vertex bisectors
draw a picture
distance = 25 cm / [cos(30ยบ)]
To find the distance from the center of gravity to each vertex of an equilateral triangular lamina, you can use the theorem of the median, which states that the center of gravity (also known as the centroid) of an equilateral triangle is located two-thirds of the distance from each vertex to the opposite side.
In this case, since each side of the equilateral triangular lamina is 50 cm, the distance from each vertex to the opposite side is half of the side length, which is 25 cm.
Now, to find the distance from the center of gravity to each vertex, we can apply the formula:
Distance from centroid to vertex = (2/3) * Distance from vertex to opposite side
Distance from centroid to vertex = (2/3) * 25 cm
Calculating the distance:
Distance from centroid to vertex = (2/3) * 25 cm
= 50/3 cm (or approximately 16.67 cm)
Therefore, the center of gravity is approximately 16.67 cm away from each vertex of the equilateral triangular lamina.