The area of a rectangular cutting board is 80 square inches. The perimeter is 36 inches. What are the dimensions of the cutting board? _____ inches by _____ inches

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The area of a rectangular cutting board is 80 square inches.  The perimeter is 36 inches. What are the dimensions of the cutting board?  _____ inches by _____ inches

Bytelearn · Accepted Answer

Define Variables: Let l be the length and w be the width of the rectangular cutting board. The area of a rectangle is given by the formula A = l * w.Area and Perimeter Formulas: The area of the cutting board is given as 80 square inches. Substitute 80 for A in the formula A = l * w. 80 = l * wSubstitute Values: The perimeter of a rectangle is given by the formula P = 2l + 2w. The perimeter of the cutting board is given as 36 inches. Substitute 36 for P in the formula P = 2l + 2w. 36 = 2l + 2wSimplify Perimeter Equation: Divide the perimeter equation by 2 to simplify. 36 / 2 = (2l + 2w) / 2 18 = l + wSolve System of Equations: We now have two equations with two variables: 80 = l * w (Area equation) 18 = l + w (Perimeter equation) We can solve this system of equations to find the values of l and w.Express Width in Terms of Length: Rearrange the perimeter equation to express w in terms of l. w = 18 - lSubstitute into Area Equation: Substitute w = 18 - l into the area equation 80 = l * w. 80 = l * (18 - l)Form Quadratic Equation: Expand the equation and move all terms to one side to form a quadratic equation. 80 = 18l - l^2 0 = l^2 - 18l + 80Factor Quadratic Equation: Factor the quadratic equation. 0 = (l - 10)(l - 8)Solve for Length: Solve for l by setting each factor equal to zero. l - 10 = 0 or l - 8 = 0 l = 10 or l = 8Find Valid Solutions: If l = 10, then w = 18 - l = 18 - 10 = 8. If l = 8, then w = 18 - l = 18 - 8 = 10. Both pairs (10, 8) and (8, 10) are valid solutions since a rectangle can have its length and width interchanged.

The area of a rectangular cutting board is $80$ square inches. The perimeter is $36$ inches. What are the dimensions of the cutting board? $\newline$ $\_\_\_$ inches by $\_\_\_$ inches

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The area of a rectangular cutting board is 808080 square inches. The perimeter is 363636 inches. What are the dimensions of the cutting board?\newline___\_\_\____ inches by ___\_\_\____ inches

The area of a rectangular cutting board is $80$ square inches. The perimeter is $36$ inches. What are the dimensions of the cutting board? $\newline$ $\_\_\_$ inches by $\_\_\_$ inches