quadratic equation

Question

The area of a rectangular book shelf is 28 square feet. The length is 2 feet longer than the width. What are the dimensions of the book shelf to the nearest tenth?

(a) Draw and label an appropriate diagram (b) Set up a quadratic equation based on the diagram (c) Solve the quadratic equation from part (b)

Answer 1

a)

_________________

| L= W+2 |

| | W

|________________ |

b) Area = L*W = (W+2)*W = W² +2W = 28 ------> W² +2W -28 =0

c) W =( -b ⁺_- squre root ( b²-4ac)) /2a

= -2 ⁺_- squre root ( 4-(4*1*-28))) /2*1

= -2 ⁺_- squre root (116) /2

= -1 ⁺_- squre root (116)

W = -1+ 10.8 =9.8 (the other answer is -11.8 but that can't be used because length cant be negative)

then L = 9.8 + 2=11.8

i hope it was helpful!