A blueprint of a bedroom has a scale of 1/4 inch is equivalent to 1 foot. If the closet measures 1/2 inch by 3/4 inch on the blueprint, what are the actual dimensions of the closet?
The bedroom closet will measure _______ feet by ________ feet.
How would I figure this out?
1/4 inch = 1 foot
1/2 inch = 2 feet
3/4 inch = _____ feet
Area = L * W
1 ft = 12 in
Scale factor:
1 ft / 1 / 4 in = 12 in / 1 / 4 in = 12 in / 0.25 in = 48
1 / 2 in β 48 = 24 in = 2 ft
3 / 4 in β 48 = 0.75 β 48 = 36 in = 3 ft
The bedroom closet will measure 2 ft by 3 ft
nothing
To figure out the actual dimensions of the closet, you can use the given scale. The scale states that 1/4 inch on the blueprint is equivalent to 1 foot in reality.
Given that the closet measures 1/2 inch by 3/4 inch on the blueprint, you need to convert these measurements to their corresponding real-world dimensions. To do this, you can set up a ratio using the given scale:
1/4 inch on the blueprint corresponds to 1 foot in reality.
So, you can write the ratio as:
(1/4) inch on the blueprint / 1 foot in reality = (1/2) inch of the closet / x feet in reality.
To solve for x, or the actual width of the closet, you can cross-multiply and solve for x:
(1/4) inch * x feet in reality = (1/2) inch * 1 foot in reality.
By multiplying both sides of the equation by 4:
x feet in reality = (1/2) inch * 1 foot in reality * 4.
Simplifying this equation gives:
x feet in reality = 2 inches * 1 foot in reality.
So, the actual width of the closet is 2 feet.
Similarly, you can set up a ratio for the length of the closet:
(1/4) inch on the blueprint / 1 foot in reality = (3/4) inch of the closet / y feet in reality.
To find y, or the actual length of the closet, you can cross-multiply and solve for y:
(1/4) inch * y feet in reality = (3/4) inch * 1 foot in reality.
By multiplying both sides of the equation by 4:
y feet in reality = (3/4) inch * 1 foot in reality * 4.
Simplifying this equation gives:
y feet in reality = 3 inches * 1 foot in reality.
So, the actual length of the closet is 3 feet.
Therefore, the bedroom closet will measure 2 feet by 3 feet.