Given
an 18 ft square with a uniform border of width x
the area of the border is 400 ft²
Find
x
Solution
The outside dimension of the square with the border added is 18+2x, so the total area of square and border is (18+2x)². Subtracting the area of the original square gives the area of the border.
... (18+2x)² -18² = 400
... 4x² +72x = 400 . . . . . simplify
... x² + 18x = 100 . . . . . . .divid by 4
... x² +18x +9² = 100 +9² . . . . complete the square
... (x +9)² = 181 . . . . . . . . .simplify
... x = √181 -9 . . . . . . . . . take the square root, subtract 9
... x ≈ 4.4536 . . . . . . . . . evaluate
The appropriate choice is ...
... c. 4.45 ft
The width should be 4.45 ft
Since there is uniform wi-dth with 18-foot ed-ges. And, the surface is 400 feet
Also here we assume the width be x
Now the equation should be
[tex](18+2x)^2 -18^2 = 400\\\\ 4x^2 +72x = 400 \\\\ x^2 + 18x = 100 \\\\ x^2 +18x +9^2 = 100 +9^2 \\\\ (x +9)^2 = 181 \\\\ x = \sqrt181 -9 \\\\[/tex]
.x ≈ 4.4536
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