For Sophia's graduation party, several tables of the same width will be arranged end to end to form a serving table with atotal area of 75 ft. The total length of the tables will be two more than three times the width. Find the length and width ofthe serving table so that Sophia can purchase the correct table cloth. Round your answers to the nearest tenth.Area: 75 ftBw + 2​

Accepted Solution

Answer:Width=4.7 ftLength=16.1 ftStep-by-step explanation:Let the width of the table to be x ftThen the length should be two more than three times the width= 2+3x ftThe area of the serving table should be 75 ft²But you know the area of this table is calculated by multiplying the length by the width of the tableHence, Area= length× widthLength=x ft  and width =2+3x ft75ft²= (x ft) × (2+3x ft)[tex]75=x*(2+3x)\\\\75=2x+3x^2\\\\3x^2+2x-75=0[/tex]Apply the quadratic formula to solve this quadratic equationThe formula is ;x= (-b ±√b²-4ac)÷2acwhere a=3, b=2 and c=-75x= (-2 ± √2²-4×3×-75)÷(2×3)x=(-2±√4+900)÷6x=(-2±√904)÷6x=(-2±30.1)÷6x=(-2+30.1)÷6=4.683⇒4.7(nearest tenth)orx=(-2-30.1)÷6= -32.1÷6=-5.35⇒ -5.4Taking the positive valuex=width =4.7 ft2+3x= length= 2+3(4.7)=16.1 ft