A drawing of a surfboard in a catalog shows its length as \(8 \frac{4}{9}\) inches. Find the actual length of the surfboard if \( \frac{1}{2} \) inch length on the drawing corresponds to \( \frac{3}{8} \) foot of actual length.
Answer (3)
2 1 in − 8 3 f t 8 8 4 in − x f t 2 1 x = 8 3 ⋅ 8 9 4 2 1 x = 8 3 ⋅ 9 76 2 1 x = 24 76 / ⋅ 2 x = 12 76 = 6 3 1 f t A n s w er : A c t u a l l e n g h t i s 6 3 1 f t .
The actual length of the surfboard is 6.33 feet.
To find the actual length of the surfboard, we first need to establish the scale given in the problem, which states that 1/2 inch in the drawing is equal to 3/8 foot in reality. The length of the surfboard in the catalog is given as 8 4/9 inches. We will convert this to an improper fraction to make calculations easier: 8 4/9 inches is the same as (72/9 + 4/9) inches, which simplifies to 76/9 inches.
Next, we set up a proportion to solve for the actual length of the surfboard:
1/2 inch / 3/8 foot = 76/9 inches / x feet
To solve for x, we cross-multiply and then divide:
(1/2) * x = (76/9) * (3/8)
x = ((76/9) * (3/8)) / (1/2)
Multiplying both sides by 2 to clear the fraction on the right:
x = 2 * ((76/9) * (3/8))
x = (152/9) * (3/8)
x = (456/72)
Finally, simplifying the fraction:
x = 6.33 feet
The actual length of the surfboard is 6 3 1 feet, calculated using proportions based on the length shown in the drawing. First, the drawing length is converted into an improper fraction, and then the ratio is used to find the actual length. This ensures an accurate conversion from the drawing to the real-world measurement.
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