Explanation:
To find the height of the triangle, we need to use the formula for the lateral surface area of a triangular prism which is:
Lateral surface area = Perimeter of the base x Height
We are given the width and length of the base which is 21 and 29 respectively. Therefore, the perimeter of the base is:
Perimeter of the base = 2 x (length + width) = 2 x (29 + 21) = 100
We are also given that the lateral surface area is 510, so we can now solve for the height:
510 = 100 x Height
Height = 510 / 100
Height = 5.1
Therefore, the height of the triangle is 5.1 units.