Question 1158846
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The square garden is s feet on a side; its area is s^2.<br>
With the path 2 feet wide around the garden, the garden plus path makes a square (s+4) feet on a side.<br>
The area of the path (376 sq ft) is the area of the garden plus path, minus the area of the garden:<br>
{{{376 = (s+4)^2 - s^2}}}
{{{376 = s^2+8s+16-s^2}}}
{{{376 = 8s+16}}}
{{{360 = 8s}}}
{{{s = 45}}}<br>
You can come up with the same equation to solve using common sense instead of formal algebra.<br>
With s the length of a side of the garden, the 2 foot wide path consists of a strip with area 2 times s on each of the four sides, plus a 2-by-2 square in each corner; the total area of the path is 376 sq ft:<br>
{{{4(2s)+4(2*2) = 376}}}
{{{8s+16 = 376}}}<br>
Same equation as before....<br>