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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)
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

User Valla
by
8.4k points

2 Answers

2 votes

Answer:

6

Explanation:

18-2.5+7 there s your helllppppppppppp

User Nogoseke
by
8.1k points
3 votes
Part A: The original triangle has a base of 18 feet and a height of 7 feet. To create the 2:5 scaled version of the deck, we can simply multiply the base and height of the original triangle by the scale factor of 2/5.

New base = 18 x 2/5 = 7.2 feet
New height = 7 x 2/5 = 2.8 feet

Therefore, the dimensions of the new deck are 7.2 feet for the base and 2.8 feet for the height.

Part B: To find the area of the original deck, we can use the formula for the area of a triangle, which is:

Area = (1/2) x base x height

Area = (1/2) x 18 x 7 = 63 square feet

To find the area of the new deck, we can use the same formula and plug in the new dimensions:

Area = (1/2) x 7.2 x 2.8 = 11.88 square feet

Therefore, the area of the original deck is 63 square feet and the area of the new deck is 11.88 square feet.

Part C: The ratio of the areas is:

63/11.88 = 5.303

The scale factor is:

2/5 = 0.4

To compare the ratio of the areas to the scale factor, we can divide the ratio of the areas by the scale factor:

5.303/0.4 = 13.2575

Therefore, the ratio of the areas is 13.2575 times the scale factor.
User Tamerlane
by
7.6k points