Question

A patient's room is 10 feet (ft) wide and 15 ft long. If all rooms are built to the same proportions, what is the length of a room that

is 18 ft wide?

A) 12 ft
B) 23 ft
C) 27 ft
D) 30 ft

Please show work

Answer 1

To solve this problem, we can use the concept of similar triangles. Since the width-to-length ratio is the same for both rooms, we can set up a proportion:

10 ft / 15 ft = 18 ft / x ft

Where x represents the length of the room that is 18 ft wide.

We can solve for x by cross multiplying:

10 ft * x ft = 15 ft * 18 ft

This simplifies to:

10x = 270

Dividing both sides by 10 gives us:

x = 27

So the answer is C) 27 ft.