The area of a rectangle is 12 square inches. The length is 5 more than twice the width. Find the length and the
width.
Thanks
Is w=-4 the correct answer?
thanks
x(2x+5)=12
2x^2+5x-12=0
(x+4)(2x-3)=0
2x-3=0
2x=3
x=3/2
3/2(2(3/2)+5)=12
3/2(3+5)=12
3/2(8)=12
24/2=12
12=12
width=3/2
length=8
To solve this problem, we can first set up equations based on the given information. Let's assume that the width of the rectangle is represented by the variable 'w'.
Given that the area of the rectangle is 12 square inches, we can write the equation:
Length × Width = Area
Length × w = 12
We are also given that the length is 5 more than twice the width. We can express this information as another equation:
Length = 2w + 5
Now we have a system of two equations:
Equation 1: Length × w = 12
Equation 2: Length = 2w + 5
We can substitute Equation 2 into Equation 1 to eliminate the 'Length' variable:
(2w + 5) × w = 12
Expanding this equation, we get:
2w^2 + 5w = 12
Rearranging the equation in standard quadratic form, we get:
2w^2 + 5w - 12 = 0
To solve this quadratic equation, we can either factor or use the quadratic formula. In this case, factoring is the simplest method. We can rewrite the equation:
(2w - 3)(w + 4) = 0
From this equation, we find that either (2w - 3) = 0 or (w + 4) = 0:
Case 1: 2w - 3 = 0
Solving for 'w' in this case, we have:
2w = 3
w = 3/2
Case 2: w + 4 = 0
Solving for 'w' in this case, we have:
w = -4
Since the width of a rectangle cannot be negative, we discard the negative value and only consider the positive value of 'w'. Therefore, the width of the rectangle is w = 3/2.
Now, substituting this value back into Equation 2 to solve for the length:
Length = 2w + 5
Length = 2(3/2) + 5
Length = 3 + 5
Length = 8
So, the length of the rectangle is 8 inches and the width is 3/2 inches.