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12 Nov 2024, 02:04
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Length of the garden bordered by the house: 48
Maximum area: 1,152
Padraig has a rectangular vegetable garden bordered by his house on one side and a picket fence on the three other sides. Currently, Padraig’s house can provide a boundary of up to 50 feet for one side of the garden and he has already used 75% of 96 feet of available picket fence to enclose the other three sides of the garden. If the picket fence can only be arranged in whole foot dimensions, what would be the length of the boundary of the garden bordered by Padraig’s house required to produce the largest possible rectangular vegetable garden should he extend the three other dimensions of it using the remaining feet of picket fence?
Select the length of the garden bordered by the house in feet and largest possible vegetable garden area in square feet after the fence is extended. Make only two selections, one in each column.
Select the length of the garden bordered by the house in feet and largest possible vegetable garden area in square feet after the fence is extended. Make only two selections, one in each column.
| Length of the garden bordered by the house | Maximum area | |
| 32 | ||
| 48 | ||
| 50 | ||
| 1,024 | ||
| 1,150 | ||
| 1,152 |
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Official Answer
Length of the garden bordered by the house: 48
Maximum area: 1,152
12 Nov 2024, 02:04
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Official Solution:
Now, test the next choice up, 48, for the length of the garden bordered by the house. If the house accounts for 48 feet of the garden, then 48 feet of fence must be used for the opposing, leaving 48 feet for the other two sides. 48 × 24 = 1,152 square feet, which would match choice F. No other area choice is larger, so the answers must be 48, and 1,152, respectively.
Correct answer:
Length of the garden bordered by the house "48"
Maximum area "1,152"
Bunuel
Plug in the choices for the length of the garden bordered by the house for the most efficient path to solving, starting with the largest value. If the house accounts for 50 feet of the garden, then 50 feet of fence must be used for the opposing side, leaving 46 feet for the other two sides. 50 × 23 = 1,150 square feet, which would match choice E.
Now, test the next choice up, 48, for the length of the garden bordered by the house. If the house accounts for 48 feet of the garden, then 48 feet of fence must be used for the opposing, leaving 48 feet for the other two sides. 48 × 24 = 1,152 square feet, which would match choice F. No other area choice is larger, so the answers must be 48, and 1,152, respectively.
Correct answer:
Length of the garden bordered by the house "48"
Maximum area "1,152"
13 Nov 2024, 01:41
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What does 75% of 96ft has been used up mean here ?
