Question

Please answer quick

Sam has a pool deck that is shaped like a triangle with a base of 15 feet and a height of 9 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 1

Answer:To find the dimensions of the new deck, we need to scale the base and height of the original deck by a factor of 3:5.

The scaled base will be:

16 feet x (3/5) = 9.6 feet

The scaled height will be:

9 feet x (3/5) = 5.4 feet

Therefore, the dimensions of the new deck will be 9.6 feet for the base and 5.4 feet for the height.

Explanation:

Answer 2

Part A:

The ratio of the sides of the new deck to the original deck is 2:5. Therefore, the base and height of the new deck can be found by multiplying the base and height of the original deck by the scale factor, which is 2/5.

Base of new deck = 15 * (2/5) = 6 feet

Height of new deck = 9 * (2/5) = 3.6 feet

Therefore, the dimensions of the new deck are 6 feet for the base and 3.6 feet for the height.

Part B:

The area of a triangle can be found by multiplying the base and height and dividing by 2.

Area of original deck = (15 * 9) / 2 = 67.5 square feet

Area of new deck = (6 * 3.6) / 2 = 10.8 square feet

Therefore, the area of the original deck is 67.5 square feet and the area of the new deck is 10.8 square feet.

Part C:

The ratio of the areas of the new deck to the original deck is:

Area of new deck / Area of original deck = 10.8 / 67.5 = 0.16

The scale factor is 2:5, or 0.4 as a decimal. The ratio of the areas is smaller than the scale factor. This means that the new deck is smaller than what it would be if it were built to scale.