A rectangular goat pen has an area of 24 square meters and a perimeter of 20 meters. What are the dimensions of the pen? _____ meters by _____ meters

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A rectangular goat pen has an area of 24 square meters and a perimeter of 20 meters. What are the dimensions of the pen?  _____ meters by _____ meters

Bytelearn · Accepted Answer

Define Area Formula:  Let l and w be the length and width of the rectangular goat pen, respectively. The area of a rectangle is given by the formula Area = l * w. Area Equation:  Given the area is 24 square meters, we have the equation 24 = l * w. Define Perimeter Formula:  The perimeter of a rectangle is given by the formula Perimeter = 2(l + w). Given the perimeter is 20 meters, we have the equation 20 = 2(l + w). Perimeter Equation:  Simplify the perimeter equation to find l + w. 20 = 2(l + w) simplifies to 10 = l + w. Simplify Perimeter:  We now have two equations: 24 = l * w and 10 = l + w. We can solve these equations simultaneously. Substitute w = 10 - l into the area equation. Substitute for Area:  Substituting gives 24 = l * (10 - l). Expanding this, we get 24 = 10l - l^2. Rearranging gives l^2 - 10l + 24 = 0. Expand and Rearrange:  Factorize the quadratic equation: (l - 6)(l - 4) = 0. So, l = 6 or l = 4. If l = 6, then w = 10 - 6 = 4. If l = 4, then w = 10 - 4 = 6.

A rectangular goat pen has an area of $24\,\text{square meters}$ and a perimeter of $20\,\text{meters}$ . What are the dimensions of the pen? $\newline$ $\_\_\_\_$ meters by $\_\_\_\_$ meters

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A rectangular goat pen has an area of 24 square meters24\,\text{square meters}24square meters and a perimeter of 20 meters20\,\text{meters}20meters. What are the dimensions of the pen?\newline____\_\_\_\_____ meters by ____\_\_\_\_____ meters

A rectangular goat pen has an area of $24\,\text{square meters}$ and a perimeter of $20\,\text{meters}$ . What are the dimensions of the pen? $\newline$ $\_\_\_\_$ meters by $\_\_\_\_$ meters