Answer:
c = 10 , d = 26
Explanation:
In the rectangular prism, we know the fact that the three faces are mutually perpendicular to each other. So, it has a rectangular base.
Given, the length and breadth of the rectangle are 8 and 6 units, and the diagonal is c.
Since it is a rectangle, length , breadth and diagonal from a right angled triangle.
So we have, c² = 6² + 8² = 36 + 64 = 100
⇒ c = 10 units
For the side face:
Length = 24 units.
As we can see, the edge of the side face is perpendicular to the base of the prism. Which means, any line on the base of the prism is perpendicular to the 24units side edge.
So we can say that , the diagonal of the rectangular base of the prism (c) is perpendicular to the 24 units side face edge.
Hence, 24 , d and c (which is 10units) form a right angled triangle
From pythagoras theorem:
d² = 24² + 10² = 576 + 100 = 676
⇒ d = 26 units