A rectangular mural is 24 feet in width and 36 feet in length. A scale drawing of the mural has a width of 8 inches. Find the length. What is the AREA, in inches, of the mural in the scale drawing?(1 point)
Responses
864 in2
864 in2
40 in2
40 in2
72 in2
72 in2
96 in2
96 in2
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To find the length of the scale drawing, we need to use the scale factor.
Scale factor = Actual length / Scale length
Scale factor = 36 feet / 8 inches = 54
Now, we can find the length of the scale drawing:
Scale length = Actual length / Scale factor
Scale length = 24 feet / 54 = 4.44 feet
So, the length of the scale drawing is 4.44 feet.
To find the area of the mural in the scale drawing, we need to find the area of the actual mural first:
Actual area = 24 feet * 36 feet = 864 square feet
Now, we can find the area in the scale drawing using the scale factor:
Scale area = Actual area / (Scale factor)^2
Scale area = 864 square feet / 54^2 = 864 / 2916 = 0.296296 square feet
Converting the area to square inches:
Scale area = 0.296296 * 144 (1 square foot = 144 square inches) = 42.66624 square inches
Therefore, the area of the mural in the scale drawing is approximately 42.67 square inches.
The closest option to this is 40 in2.