We appreciate your visit to An engineer has a 40 1 scale drawing of a bridge The dimensions of the scaled bridge deck are 42 inches by four and four. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Answer: 840 ft²
Step-by-step explanation:
The engineer has a 40:1 scale drawing, which means that every 1 inch on the drawing represents 40 inches in our real-life model. To find the actual dimensions of the bridge deck, we can multiply the dimensions on the drawing by a scale factor of 40.
Actual length = 42 inches × 40 = 1680 inches
Actual width = (4 + 4/5) inches × 40 = (9/5) inches × 40 = 72 inches
Now that we have the actual dimensions in inches, we can convert them to feet because we want the area in square feet.
Actual length in feet = 1680 inches / 12 = 140 feet
Actual width in feet = 72 inches / 12 = 6 feet
Now, we need the area of the deck.
Area = Length × Width
Area = 140 feet × 6 feet = 840 square feet
So, the area of the deck is 840 square feet.
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Answer:
(c) 2240 square feet
Step-by-step explanation:
You want the actual area of a bridge deck, given that a 1:40 drawing represents it as 42 inches by 4 4/5 inches.
Scale
The scale factor tells you the actual dimensions are 40 times the drawing dimensions. That means the actual dimensions in inches are ...
length: (42 in)·40 = 1680 in
width: (4 4/5 in)·40 = 192 in
Feet
Converting these dimensions to feet, we find them to be ...
length: (1680 in)/(12 in/ft) = 140 ft
width: (192 in)/(12 in/ft) = 16 ft
Area
The area of the actual bridge deck is the product of its length and width:
A = LW
A = (140 ft)(16 ft) = 2240 ft²
The area of the actual bridge deck is 2240 square feet.
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Additional comment
The attached calculation shows the area in square inches. The actual area is that area multiplied by the square of the scale factor. The division by 144 comes from 144 in²/ft² to convert square inches to square feet.
A drawing scale usually is expressed as (drawing units) : (world units). We're pretty sure a bridge drawing scale would be 1:40, rather than 40:1.
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