Answer:
7 ft ×6 ft
Step-by-step explanation:
Area of rectangle= length ×width
Let the length and width of the rectangle be L and W ft respectively.
Form 2 equations using the given information:
LW= 42 -----(1)
L= 3W -11 -----(2)
Substitute (2) into (1):
(3W -11)(W)= 42
Expand:
3W² -11W= 42
3W² -11W -42= 0
[tex]\boxed{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }[/tex]
Applying quadratic formula:
[tex]W= \frac{ - ( - 11)± \sqrt{( - 11) {}^{2} - 4(3)( - 42) } }{2(3)} [/tex]
[tex]W= \frac{ 11± \sqrt{625 } }{6} [/tex]
[tex]W= \frac{ 11± 25}{6} [/tex]
W= 6 or W= [tex] - \frac{7}{3} [/tex] (reject)
Substitute W= 6 into (1):
L(6)= 42
L= 42 ÷6
L= 7
Thus the dimensions of the rectangle is 7 ft ×6 ft.
