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.