Question

A backyard playhouse was designed after a real house, using a scale tactor of 3:5. the ceilings in the playhouse are 6 foot tall, how high are the ceilings in the actual house?

Answer 1

The height of the actual house ceilings is found by setting up a proportion using the scale factor of 3:5. Since the playhouse ceilings are 6 feet tall, the actual house's ceilings would be 21.6 feet tall.

Step-by-step explanation:

To determine the height of the actual house ceilings based on the scale of the playhouse, you would set up a proportion using the scale factor. In this case, the scale factor given is 3:5, which means for every 3 units of measurement in the playhouse, there are 5 corresponding units in the real house. If the playhouse ceilings are 6 feet tall, we can set up the following proportion to find the height of the ceilings in the real house:

3 (playhouse units) / 5 (real house units) = 6 feet (height of playhouse ceilings) / x feet (height of real house ceilings)

To solve for x, you multiply both sides by x and divide by 3 to isolate x:

5x = 18
x = 18 / 5
x = 3.6

So, the ceilings in the actual house are 3.6 times the height of the playhouse ceilings. Plugging in the playhouse ceiling height:

x = 3.6 * 6 feet
x = 21.6 feet

Therefore, the ceilings in the actual house are 21.6 feet tall.