The length and width of the rectangle is 12 feet and 5.5 feet respectively given that the area of a rectangle is 66 feet², and the length of the rectangle is 1 feet more than twice the width. This can be obtained by finding algebraic expression for length by assuming width to be b and solving the quadratic equation formed after substituting it in the formula of area of rectangle.
Area of a rectangle,
A= l × b, where A is the area, l is the length and b is the width.
Let us assume that width of the rectangle is b.
Given that, length of the rectangle is 1 feet more than twice the width
⇒ l = 2b+1 is the required expression.
Given that A= 66 feet²
In the formula, A= l × b we can substitute the expression for length.
66=(2b+1)b
2b²+b=66
⇒ 2b²+b-66=0
The quadratic equation can be solved using splitting the middle term,
2b²+12b-11b-66=0
2b(b+6)-11(b+6)=0
(2b-11)(b+6)=0
b=11/2 or b= - 6
Taking positive value of b, b=11/2⇒b=5.5 feet
Substitute for length, l = 2b+1 = 2(11/2)+1=11+1 =12 ⇒l = 12 feet
Hence the length and width of the rectangle is 12 feet and 5.5 feet respectively given that the area of a rectangle is 66 feet², and the length of the rectangle is 1 feet more than twice the width.
Learn more about solving quadratic equation here:
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