Question

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 fifths inches. What is the area of the actual bridge deck in square feet?

18 square feet
1,872 square feet
2,240 square feet
322,560 square feet

Answer 1

Answer: 840 ft²

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.

Answer 2

(c) 2240 square feet

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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