The area of a photograph is 40 square inches. The perimeter is 26 inches. What are the dimensions of the photograph? _____ inches by _____ inches

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The area of a photograph is 40 square inches.  The perimeter is 26 inches. What are the dimensions of the photograph?  _____ inches by _____ inches

Bytelearn · Accepted Answer

Area Equation: Let's denote the length and width of the photograph as l and w respectively. Since the photograph is a rectangle, the area A is given by A = l * w. Given the area of the photograph is 40 square inches, we have the equation: 40 = l * wPerimeter Equation: The perimeter P of a rectangle is given by P = 2l + 2w. Given the perimeter of the photograph is 26 inches, we have the equation: 26 = 2l + 2wSolving System of Equations: To find the dimensions l and w, we need to solve the system of equations: 1. 40 = l * w 2. 26 = 2l + 2w Let's simplify the second equation by dividing all terms by 2: 13 = l + wExpressing Width in Terms of Length: Now we have two equations: 1. 40 = l * w 2. 13 = l + w From the second equation, we can express w in terms of l: w = 13 - lQuadratic Equation: Substitute w from the fourth step into the first equation: 40 = l * (13 - l) This gives us a quadratic equation: 40 = 13l - l^2 Rearranging the terms, we get: l^2 - 13l + 40 = 0Factoring Quadratic Equation: We need to factor the quadratic equation: l^2 - 13l + 40 = (l - 5)(l - 8) = 0 This gives us two possible solutions for l: l = 5 or l = 8First Solution: l = 5: If l = 5, then substituting back into w = 13 - l gives us: w = 13 - 5 w = 8Second Solution: l = 8: If l = 8, then substituting back into w = 13 - l gives us: w = 13 - 8 w = 5Valid Solutions: Both solutions (l = 5, w = 8) and (l = 8, w = 5) are valid since they are interchangeable (length and width can be swapped for a rectangle). They both satisfy the original equations for area and perimeter.

The area of a photograph is $40$ square inches. The perimeter is $26$ inches. What are the dimensions of the photograph? $\newline$ $\_\_\_$ inches by $\_\_\_$ inches

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The area of a photograph is 404040 square inches. The perimeter is 262626 inches. What are the dimensions of the photograph?\newline___\_\_\____ inches by ___\_\_\____ inches

The area of a photograph is $40$ square inches. The perimeter is $26$ inches. What are the dimensions of the photograph? $\newline$ $\_\_\_$ inches by $\_\_\_$ inches