Answer:
w = 10
l=31
Step-by-step explanation:
To calculate an area of a rectangle, use the formula A=l*w. We know the length is 1 ft less than three times the width. So l = 3w - 1. So the area is A= (3w-1)*w.
We also know the area is 310. Substitute this value for A and solve.
[tex]310 = (3w-1)(w)\\310 = 3w^2-w\\3w^2+w-310 = 0[/tex]
To solve the quadratic, use the quadratic formula:
[tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Here a=3, b=-1 and c=-310.
[tex]w=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\w=\frac{-(-1)+/-\sqrt{(-1)^2-4(3)(-310)} }{2(3)} \\w=\frac{1+/-\sqrt{1+3720} }{6} \\w=\frac{1+/-\sqrt{3721} }{6} \\w=\frac{1+/-61 }{6} \\w=\frac{1+61 }{6}=\frac{62}{6}=10.333... \\and\\w=\frac{1-61 }{6} =\frac{-60}{6}=-10[/tex]
This is w and must be positive since it is distance. So w=10.333....
To find l, substitute into l = 3w-1.
l=3(10.333..)-1
l=31-1 = 30
