The length of a rectangle is 2 cm more that 5 times it's width. If the area of the rectangle is 84 cm^2 find the dimensions of the rectangle to the nearest thousandth.
This is what I have..is it rihgt?
5x^2+5x+2-84
5x^2+5x-82=0
-5+-the square root of 5^2-4(5)(-82)/2(5)
-5+- the square root of 25+1640/10
-5+- the square root of 1665/10
L=2+5x
L=2+5(3.58)
L=20.06 cm
W=3.58 Cm
I don't know how you got your equation.
let the width be x
then the length is 5x+2 and
x(5x+2)=84
5x^2 + 2x - 84 = 0
now solve that.
(Igot x=3.9 and a negative x value)
To solve the problem, you need to follow the steps correctly. Let's break it down together:
Step 1: Understand the problem.
We are given that the length of a rectangle is 2 cm more than 5 times its width. The area of the rectangle is 84 cm^2. We need to find the dimensions of the rectangle.
Step 2: Assign variables.
Let's assign "L" to represent the length and "W" to represent the width of the rectangle.
Step 3: Translate the given information into equations.
We are given that the length of the rectangle is 2 cm more than 5 times its width. Using our variables, we can write this as:
L = 5W + 2 (equation 1)
We are also given that the area of the rectangle is 84 cm^2. The formula for the area of a rectangle is A = L * W. Substituting the given values, we get:
84 = L * W (equation 2)
Step 4: Solve the system of equations.
We have two equations: equation 1 and equation 2. We can solve them simultaneously to find the values of L and W.
First, let's substitute equation 1 into equation 2:
84 = (5W + 2) * W
Expanding the equation:
84 = 5W^2 + 2W
Rearranging the equation:
5W^2 + 2W - 84 = 0
Step 5: Solve the quadratic equation.
To solve the quadratic equation, you can use factoring, completing the square, or the quadratic formula. In this case, it is easier to use the quadratic formula.
The quadratic formula is given as: x = (-b ± √(b^2 - 4ac)) / (2a)
In our quadratic equation, a = 5, b = 2, and c = -84.
Finding the discriminant:
The discriminant is the value inside the square root: b^2 - 4ac
Discriminant = (2^2) - (4 * 5 * -84)
Discriminant = 4 + 1680
Discriminant = 1684
Substituting the values into the quadratic formula:
W = (-2 ± √1684) / (2 * 5)
Calculating the square root of the discriminant:
√1684 ≈ 41.0487515
Simplifying the equation:
W = (-2 ± 41.0487515) / 10
Solving for the positive value:
W = (41.0487515 - 2) / 10
W ≈ 3.90487515
Step 6: Calculate the length.
Now that we have the value of W, we can substitute it back into equation 1 to find L:
L = 5W + 2
L = 5(3.90487515) + 2
L ≈ 19.52437575
So, the approximated dimensions of the rectangle to the nearest thousandth are:
Length (L) ≈ 19.524 cm
Width (W) ≈ 3.905 cm