A rectangular shaped desk has a length of 36 inches and a width of 16 inches. A desk with a similar shape has a width of 24 inches. What is the length of this desk?
To find the length of the second desk, we can use the concept of proportional relationships between the dimensions of similar shapes.
Let's set up a ratio using the dimensions of the two desks:
Length of first desk : Width of first desk = Length of second desk : Width of second desk
Substituting the known values:
36 inches : 16 inches = Length of second desk : 24 inches
To solve for the length of the second desk, we can cross multiply:
36 inches × 24 inches = Length of second desk × 16 inches
864 square inches = Length of second desk × 16 inches
Now, let's isolate the length of the second desk by dividing both sides of the equation by 16 inches:
(864 square inches) / (16 inches) = Length of second desk
Simplifying the expression:
54 inches = Length of second desk.
Therefore, the length of the second desk is 54 inches.