a swimming pool is shaped like a square. the distance between each of the pools corners is 30 feet. a pool…
a swimming pool is shaped like a square. the distance between each of the pools corners is 30 feet. a pool cover with dimensions of 25 feet by 40 feet is used to protect the pool during the winter season. will the cover protect the entire pool? explain.\n\nselect the correct choice below.\n\na. yes, because the area of the pool cover is greater than the area of the pool.\n\nb. no, because the pool cover is longer than the pool.\n\nc. no, because the pool cover is not as wide as the pool.
Answer
Explanation:
Step1: Find side length of square pool
The distance between corners (diagonal) of square pool is 30 feet. For a square with side length ( s ), diagonal ( d = s\sqrt{2} ). So, ( s=\frac{d}{\sqrt{2}}=\frac{30}{\sqrt{2}}\approx21.21 ) feet. The side length of the pool is approximately 21.21 feet.
Step2: Analyze pool cover dimensions
The pool cover is 25 feet by 40 feet. The width (25 ft) and length (40 ft) of the cover: the pool's side is ~21.21 ft. The cover's width (25 ft) is more than pool's side, but we also check if the cover can cover the square. Wait, actually, the pool is a square, so its side is ~21.21 ft. The cover is 25x40, so its area is ( 25\times40 = 1000 ) sq ft. The pool's area is ( s^2=\left(\frac{30}{\sqrt{2}}\right)^2=\frac{900}{2}=450 ) sq ft. Now check the options:
- Option A: Area of cover (1000) > area of pool (450), so cover can protect.
- Option B: "longer" is not relevant; cover's length (40) is longer than pool's side (~21.21), but that's not the reason.
- Option C: Cover's width (25) is more than pool's side (~21.21), so "not as wide" is wrong.
So the correct reasoning is area of cover > area of pool.
Answer:
A. Yes, because the area of the pool cover is greater than the area of the pool.