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A rectangular sandbox is surrounded on all sides by a strip of grass that is feet wide on all sides. The length of the sandbox is 4 feet more than the width, and the total area for the sandbox and the grass is 189 square feet. Find the dimensions of the sandbox.

Sagot :

Mhanifaidn

Answer:

  • 13.9 ft, 9.9 ft

Step-by-step explanation:

Sandbox has dimensions x and y.

We have:

  • x = y + 4
  • (x + 2)(y + 2) = 189, (one foot grass from both sides adds 2 ft)

Substitute x and solve for y:

  • (y + 4 + 2)(y + 2) = 189
  • (y + 6)(y + 2) = 189
  • y² + 8y + 12 = 189
  • y² + 8y + 16 = 193
  • (y + 4)² = 193
  • y + 4 = √193 (taken positive root only as distance can't be negative)
  • y + 4 ≈ 13.9
  • y = 9.9

Find x:

  • x = 9.9 + 4 = 13.9
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