A rectangular concrete patio has a perimeter of 36 meters. Its area is 80 square meters. What are the dimensions of the patio? _____ meters by _____ meters

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A rectangular concrete patio has a perimeter of 36 meters.  Its area is 80 square meters. What are the dimensions of the patio?  _____ meters by _____ meters

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Rectangle Perimeter Equation:  Let l and w be the length and width of the rectangle, respectively. The perimeter of a rectangle is given by P = 2l + 2w. Given P = 36 meters, we can write the equation: 2l + 2w = 36 Simplify by dividing everything by 2: l + w = 18 Rectangle Area Equation:  We also know the area of the rectangle is A = lw and it's given as 80 square meters. So, we have the equation: lw = 80 Solving for Width:  From the perimeter equation l + w = 18, solve for one variable in terms of the other. Let's solve for w: w = 18 - l Substitute into Area Equation:  Substitute w = 18 - l into the area equation lw = 80: l(18 - l) = 80 Expand the equation: 18l - l^2 = 80 Rearrange to form a quadratic equation: l^2 - 18l + 80 = 0 Quadratic Equation Solution:  Solve the quadratic equation using the quadratic formula, l = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 1, b = -18, and c = 80: l = (-(-18) ± sqrt((-18)^2 - 4*1*80)) / (2*1) l = (18 ± sqrt(324 - 320)) / 2 l = (18 ± sqrt(4)) / 2 l = (18 ± 2) / 2 l = 10 or l = 8

A rectangular concrete patio has a perimeter of $36\,\text{meters}$ . Its area is $80\,\text{square meters}$ . What are the dimensions of the patio? $\newline$ $\_\_\_\_$ meters by $\_\_\_\_$ meters

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A rectangular concrete patio has a perimeter of 36 meters36\,\text{meters}36meters. Its area is 80 square meters80\,\text{square meters}80square meters. What are the dimensions of the patio?\newline____\_\_\_\_____ meters by ____\_\_\_\_____ meters

A rectangular concrete patio has a perimeter of $36\,\text{meters}$ . Its area is $80\,\text{square meters}$ . What are the dimensions of the patio? $\newline$ $\_\_\_\_$ meters by $\_\_\_\_$ meters