C.SINCE WE ARE TRYING TO FIND THE WIDTH OF THE DECK, LET X= THE WI...

37. c.Since we are trying to find the width of the deck, let x= the width of the deck. Therefore,x+ x+ 20or 2x+ 20 is the width of the entire figure. In the same way,x+ x+ 28 or 2x+ 28 is the length of theentire figure.The area of a rectangle is length ×width, so use A = l ×w.Substitute into the equation: 884 = (2x+ 20)(2x+ 28)Multiply using FOIL: 884 = 4x

²

+ 56x+ 40x+ 560Combine like terms: 884 = 4x

²

+ 96x+ 560Subtract 884 from both sides: 884 – 884 = 4x

²

+ 96x+ 560 – 884 0 = 4x

²

+ 96x– 324Divide each term by 4: 0 = x

²

+ 24x– 81Factor the trinomial: 0 = (x+ 27)(x– 3)Set each factor equal to zero and solve: x+ 27 = 0 or x – 3 = 0x= –27 x= 3Since we are solving for a length, the solution of –27 must be rejected. The width of the deck is 3 feet.