Mathematics: A square plot of land will be fully used for a square swimming pool with a 5 foot wide walkway around it. The area of the entire plot, including the walkway, is A square feet. Which expression gives the length of the pool?

574649 divided by 58 is 9907.74Step-by-step explanation:...

A square plot of land will be fully used for a

terrybrown5391

10.02.2022

The expression that gives the length of the pool is $\sqrt{A}$ - 5

Step-by-step explanation:

Assume that the length of the pool is x feet

∵ The length of the pool is x feet

∵ The wide of the walkway around the pool is 5 feet

∴ The total length of the pool with the walkway = (x + 5) feet

∵ The area of the entire plot, including the walkway, is A square feet

∴ The area of the entire plot, including the walkway = A feet²

∵ The area of the square = (length)²

→ Substitute the length by (x + 5)

∴ The area of the entire plot, including the walkway = (x + 5)² feet²

→ Equate it by A

∴ A = (x + 5)²

→ To find x take square root for both sides

∵ $\sqrt{A}$ = $\sqrt{(x+5)^{2}}$

→ Cancel the square root of the right side by power 2

∴ $\sqrt{A}$ = x + 5

→ Subtract 5 from both sides

∵ $\sqrt{A}$ - 5 = x + 5 - 5

∴ $\sqrt{A}$ - 5 = x

→ x represents the length of the pool

∴ The length of the pool is $\sqrt{A}$ - 5 feet

∴ The expression that gives the length of the pool is $\sqrt{A}$ - 5

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