Answer:
A. 80 square feet
B. four options are 8×10 ft, 10×8 ft, 5×16 ft, 7 1/2×10 2/3 ft
Step-by-step explanation:
The area of Jason's deck can be found using the formula for the area of a trapezoid. The dimensions of Sarah's deck can be found by considering the factors of the area of Jason's deck.
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A. Jason
The area of a trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
where b1 and b2 are the base lengths, and h is the perpendicular distance between them. Here, we have b1 = 16 ft, b2 = 4 ft, h = 8 ft, so the area is ...
A = 1/2(16 ft +4 ft)(8 ft) = 80 ft²
The area of Jason's deck is 80 square feet.
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B. Sarah
The integer factor pairs of 80 are ...
80 = 1×80 = 2×40 = 4×20 = 5×16 = 8×10
For non-integer factor pairs, one can be found from the other by dividing 80 by the one given:
for a 7 1/2 ft deck, the other dimension is 80/7.5 = 10.66666... = 10 2/3
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For a nearly square deck, Sarah could make hers ...
8 feet wide and 10 feet long
10 feet wide and 8 feet long
One with integer dimensions that would be somewhat narrower would be ...
5 feet wide and 16 feet long
If Sarah uses non-integer dimensions, she could make her deck ...
7 1/2 ft wide and 10 2/3 ft long
