A rectangular garden whose width is 4 meters less than its length has an area of 57 square meters. Find the dimensions of the garden to the nearest tenth of a meter.

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Define Variables: Let's call the length of the garden L meters and the width W meters. We know that W = L - 4. The area of the garden is given as 57 square meters, so we can write the equation L * W = 57.Area Equation: Now we substitute W with L - 4 in the area equation: L * (L - 4) = 57.Expand Equation: Expanding the equation gives us L^2 - 4L = 57.Quadratic Equation: To find the value of L, we need to solve the quadratic equation. We move all terms to one side to set the equation to zero: L^2 - 4L - 57 = 0.Quadratic Formula: We can solve the quadratic equation by factoring, completing the square, or using the quadratic formula. The quadratic formula is L = (-b ± √(b^2 - 4ac)) / (2a). In our equation, a = 1, b = -4, and c = -57.Substitute Values: Plugging the values into the quadratic formula gives us L = (4 ± √((-4)^2 - 4*1*(-57))) / (2*1).Simplify Square Root: Simplifying inside the square root: L = (4 ± √(16 + 228)) / 2.Calculate Solutions: Further simplification gives us L = (4 ± √244) / 2.Discard Negative Solution: Calculating the square root of 244 gives us approximately 15.62. So, L = (4 ± 15.62) / 2.Calculate Length: We have two possible solutions for L: L = (4 + 15.62) / 2 or L = (4 - 15.62) / 2. Since a length can't be negative, we discard the second solution.Calculate Width: Calculating the positive solution gives us L = (4 + 15.62) / 2 = 19.62 / 2 = 9.81 meters.Now we find the width using the relationship W = L - 4: W = 9.81 - 4 = 5.81 meters.

A rectangular garden whose width is $4$ meters less than its length has an area of $57$ square meters. Find the dimensions of the garden to the nearest tenth of a meter.

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A rectangular garden whose width is $4$ meters less than its length has an area of $57$ square meters. Find the dimensions of the garden to the nearest tenth of a meter.