The area of a rectangular restaurant kitchen is 70 square meters. The perimeter is 34 meters. What are the dimensions of the kitchen? _____ meters by _____ meters

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The area of a rectangular restaurant kitchen is 70 square meters.  The perimeter is 34 meters. What are the dimensions of the kitchen?  _____ meters by _____ meters

Bytelearn · Accepted Answer

Rectangle Area Formula:  Let l and w be the length and width of the rectangular kitchen, respectively. We know the area A of a rectangle is given by A = l * w. Given area: 70 square meters. 70 = l * w Rectangle Perimeter Formula:  The perimeter P of a rectangle is given by P = 2l + 2w. Given perimeter: 34 meters. 34 = 2l + 2w Simplify Perimeter Equation:  We can simplify the perimeter equation to make one variable the subject. Divide the perimeter equation by 2: 17 = l + w Now, substitute w = 17 - l into the area equation: 70 = l * (17 - l) Solve Quadratic Equation:  Solve the quadratic equation 70 = l * (17 - l). Expanding it gives: 70 = 17l - l^2 Rearrange to form a standard quadratic equation: l^2 - 17l + 70 = 0 Factorize Quadratic Equation:  Factorize the quadratic equation: (l - 7)(l - 10) = 0 So, l = 7 or l = 10. If l = 7, then w = 17 - 7 = 10. If l = 10, then w = 17 - 10 = 7. Both pairs (7, 10) and (10, 7) are valid as dimensions of the rectangle.

The area of a rectangular restaurant kitchen is $70\,\text{square meters}$ . The perimeter is $34\,\text{meters}$ . What are the dimensions of the kitchen? $\newline$ $\_\_\_\_$ meters by $\_\_\_\_$ meters

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The area of a rectangular restaurant kitchen is 70 square meters70\,\text{square meters}70square meters. The perimeter is 34 meters34\,\text{meters}34meters. What are the dimensions of the kitchen?\newline____\_\_\_\_____ meters by ____\_\_\_\_____ meters

The area of a rectangular restaurant kitchen is $70\,\text{square meters}$ . The perimeter is $34\,\text{meters}$ . What are the dimensions of the kitchen? $\newline$ $\_\_\_\_$ meters by $\_\_\_\_$ meters