The scale drawing of a deck that Mr. Ford is building measures 15 cm by 21 cm. Each 3 cm on the scale drawing equals 5 feet. What are the actual dimensions of the deck? after you select your answer, explain
Responses
A 15 feet x 21 feet15 feet x 21 feet
B 16 feet x 20 feet16 feet x 20 feet
C 20 feet x 30 feet20 feet x 30 feet
D 25 feet x 35 feet25 feet x 35 feet
E 35 feet x 45 feet
A) 15 feet x 21 feet
To find the actual dimensions of the deck, we need to first determine the scale factor. Since each 3 cm on the scale drawing equals 5 feet in reality, we can set up a ratio:
3 cm = 5 feet
15 cm = x feet
Cross multiplying, we get:
3x = 75
x = 25
So, the actual width of the deck is 25 feet.
Using the same process for the length:
3 cm = 5 feet
21 cm = y feet
Cross multiplying, we get:
3y = 105
y = 35
So, the actual length of the deck is 35 feet.
Therefore, the actual dimensions of the deck are 25 feet x 35 feet.
explain
To find the actual dimensions of the deck, we have to first determine the scale factor by comparing the measurements on the scale drawing to the actual measurements. Here, it is given that each 3 cm on the scale drawing equals 5 feet in reality.
Given that the scale drawing measures 15 cm by 21 cm, we need to find the actual dimensions using the scale factor.
For the width:
On the scale drawing, 3 cm represents 5 feet.
So, 15 cm represents x feet (the unknown actual width).
By setting up a proportion: 3/5 = 15/x, we can solve for x. Solving this gives x = 25 feet.
Hence, the actual width of the deck is 25 feet.
For the length:
On the scale drawing, 3 cm represents 5 feet.
So, 21 cm represents y (the unknown actual length).
Again, setting up a proportion: 3/5 = 21/y, we can solve for y. Solving this gives y = 35 feet.
Therefore, the actual dimensions of the deck are 25 feet by 35 feet.