The perimeter of a rectangular living room is 34 meters. The area is 72 square meters. What are the dimensions of the living room? _____ meters by _____ meters

Question

The perimeter of a rectangular living room is 34 meters.  The area is 72 square meters. What are the dimensions of the living room?  _____ meters by _____ meters

Bytelearn · Accepted Answer

Define Perimeter Equation:  Let the length be l meters and the width be w meters. The perimeter of a rectangle is given by P = 2l + 2w. Simplify Perimeter Equation:  Given the perimeter is 34 meters, we set up the equation 2l + 2w = 34. Simplify this by dividing everything by 2: l + w = 17. Define Area Equation:  The area of a rectangle is given by A = lw. We know the area is 72 square meters, so lw = 72. Solve Equations Simultaneously:  We now have two equations: l + w = 17 and lw = 72. Solve these simultaneously. Start by expressing w from the first equation: w = 17 - l. Substitute and Simplify:  Substitute w = 17 - l into the area equation: l(17 - l) = 72. This simplifies to 17l - l^2 = 72. Rearrange to form a quadratic equation: l^2 - 17l + 72 = 0. Factorize Quadratic Equation:  Factorize the quadratic equation: (l - 8)(l - 9) = 0. So, l = 8 or l = 9. Find Valid Dimensions:  If l = 8, then w = 17 - 8 = 9. If l = 9, then w = 17 - 9 = 8. Both pairs (8, 9) and (9, 8) are valid as dimensions.

The perimeter of a rectangular living room is $34$ meters. The area is $72$ square meters. What are the dimensions of the living room? $\newline$ $\_\_\_$ meters by $\_\_\_$ meters

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The perimeter of a rectangular living room is $34$ meters. The area is $72$ square meters. What are the dimensions of the living room? $\newline$ $\_\_\_$ meters by $\_\_\_$ meters