Question
Sam has a deck that is shaped like a triangle with a base of 18 feet and a height of 7 feet. He plans to build a 2:5 scaled version of the deck next to his horse's water trough. Part A: What are the dimensions of the new deck, in feet? Show every step of your work. (4 points) Part B: What is the area of the original deck and the new deck, in square feet? Show every step of your work. (4 points) Part C: Compare the ratio of the areas to the scale factor. Show every step of your work. (4 points)
Answer
{"Part A":{"New Dimensions":"7.2ft (base) by 2.8ft (height)"}, "Part B":{"Area of original deck":"63 sq.ft.","Area of new deck":"10.08 sq.ft."}, "Part C":{"Ratio of Areas to scale":"0.16"}}
- For Part A: To find the dimensions of the new deck, we need to find the new base and height of the triangle based on the given scale factor. Since the scale factor is 2:5, we can find the new base and height by multiplying the original base and height by 2/5.
- For Part A: New Base = 18ft * (2/5) = 7.2ft, New Height = 7ft * (2/5) = 2.8ft. Therefore, the new dimensions of the deck are 7.2ft (base) by 2.8ft (height).
- For Part B: To find the area of the original triangle, we use the formula: (base * height)/2
- For Part B: Area of Original Deck = (18ft * 7ft)/2 = 63 sq.ft.
- For Part B: To find the area of the new triangle, we use the formula: (new base * new height)/2.
- For Part B: Area of New Deck = (7.2ft * 2.8ft)/2 = 10.08 sq.ft.
- For Part C: To compare the ratio of the areas to the scale factor, we divide the area of the new deck by the area of the original deck.
- For Part C: Ratio of Areas = (area of new deck)/(area of original deck) = 10.08 sq.ft./63 sq.ft. = 0.16.