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

Respuesta :

lucic

Answer:

Width=4.7 ft

Length=16.1 ft

Step-by-step explanation:

Let the width of the table to be x ft

Then the length should be two more than three times the width= 2+3x ft

The area of the serving table should be 75 ft²

But you know the area of this table is calculated by multiplying the length by the width of the table

Hence, Area= length× width

Length=x ft  and width =2+3x ft

75ft²= (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 equation

The formula is ;

x= (-b ±√b²-4ac)÷2ac

where a=3, b=2 and c=-75

x= (-2 ± √2²-4×3×-75)÷(2×3)

x=(-2±√4+900)÷6

x=(-2±√904)÷6

x=(-2±30.1)÷6

x=(-2+30.1)÷6=4.683⇒4.7(nearest tenth)

or

x=(-2-30.1)÷6= -32.1÷6=-5.35⇒ -5.4

Taking the positive value

x=width =4.7 ft

2+3x= length= 2+3(4.7)=16.1 ft