Answer :
The height of the triangular prism pedestal is calculated by dividing the area of the cloth (192 square centimeters) by the perimeter of the right triangle base (28 centimeters), which results in approximately 6.857 centimeters.
The problem involves finding the height of a triangular prism, given that it has been wrapped with a rectangular cloth that covers its lateral surface area but not its bases. To find the height of the pedestal (prism), we first need to recognize that the bases of the prism are right triangles. As the side lengths of the base triangle are given as 12 centimeters, 16 centimeters, and 20 centimeters, we can tell that it is a Pythagorean triplet, which confirms that it is indeed a right triangle with the 20 cm side being the hypotenuse.
To solve the problem, we must calculate the perimeter of the base triangle, which will also serve as the length of the rectangle made by the cloth when it is unwrapped. The perimeter of the right triangle (excluding the hypotenuse) is 12 cm + 16 cm = 28 cm. Since we are given the area of the cloth is 192 square centimeters, and the area of a rectangle is the product of its length and width, the width of the cloth rectangle, which corresponds to the height of the pedestal, can be found by dividing the area of the cloth by the perimeter of the triangular base.
Therefore, the height of the prism, h, is given by Area of cloth / Perimeter of triangular base = 192 cm² / 28 cm, which results in a height of 6.857 centimeters (rounded to three decimal places).
Based on the question presented, it doesn't asked what to do. It just presented the given and the dimension of the triangular prism.
