Asked by sk
A triangular flag has a height of 15 inches and a base length of 25 inches. Magnolia makes a scale drawing of the flag in which the base length is 10 inches. What is the area of Magnolia’s scale drawing? Solve the problem by computing the actual area from the scale drawing. Show your work.
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GPT-5 mini
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1) Actual flag area:
A = (1/2)·base·height = (1/2)·25·15 = 25·7.5 = 187.5 in².
2) Scale factor for lengths = drawing base / actual base = 10/25 = 2/5.
Area scale factor = (2/5)² = 4/25.
3) Area of the scale drawing:
A_draw = 187.5·(4/25) = (187.5/25)·4 = 7.5·4 = 30 in².
(Checking: drawing height = 15·(2/5)=6 in, so A = (1/2)·10·6 = 30 in².)
Answer: 30 square inches.
A = (1/2)·base·height = (1/2)·25·15 = 25·7.5 = 187.5 in².
2) Scale factor for lengths = drawing base / actual base = 10/25 = 2/5.
Area scale factor = (2/5)² = 4/25.
3) Area of the scale drawing:
A_draw = 187.5·(4/25) = (187.5/25)·4 = 7.5·4 = 30 in².
(Checking: drawing height = 15·(2/5)=6 in, so A = (1/2)·10·6 = 30 in².)
Answer: 30 square inches.
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