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 on the drawing corresponds to \(\frac{3}{8}\) foot of actual length.

(1/2) i _ _ _ (3/8) f => 1 i _ _ _ (3/4) f => 8 i _ _ _ 6 f; (1/2) i _ _ _ (3/8) f => (8/9)(1/2) i _ _ _ (8/9)(3/8) f =>(4/9) i _ _ _(1/3) f; 8 4/9 f _ _ _ 6 1/3 f.

Answered by crisforp | 2024-06-10

The actual length of the surfboard, scaled up from the drawing length of 8 4/9 inches using the given scale of 1/2 inch to 3/8 foot, is approximately 6 feet 4 inches.
To find the actual length of the surfboard, we first need to set up a proportional relationship based on the scale provided. According to the question, the drawing of the surfboard is 8 4/9 inches long and every 1/2 inch in the drawing corresponds to 3/8 foot in actual length.
First, we convert 8 4/9 inches to an improper fraction: 8 x 9 + 4 = 76/9 inches. We can then write the proportion as follows:

1/2 inch (drawing) = 3/8 foot (actual)
76/9 inches (drawing) = x feet (actual)

Now we solve the proportion:
= (1/2 inches) / (3/8 feet) = (76/9 inches) / x feet
To find x , we cross-multiply and solve for x :
= (1/2) x x = (76/9) x (3/8)
First, simplify the fractions on the right side:
x = (76/9) x (3/8) x (2/1)
Then, perform the multiplication:
x = 228/36
Finally, simplify the fraction to its lowest terms to find the actual length:
x = 6.33 feet, or 6 feet 4 inches (since 0.33 feet is approximately 4 inches)

Answered by AliciaAugello | 2024-06-24

The actual length of the surfboard is 76 inches, which converts to 6 feet and 3 inches. This was derived from the catalog length and the scale of the drawing. Each inch in the drawing corresponds to 9 inches of actual length.
;

Answered by crisforp | 2024-12-24