The area of a rectangle is 20 square inches. If the length is 4 inches less than 6 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.
Guide On Rating System
Vote
Let's assume the width of the rectangle is x inches.
According to the given information, the length of the rectangle is 6x - 4 inches.
The area of a rectangle is given by the formula: length * width.
So, we can set up the equation: (6x - 4) * x = 20
Expanding this equation, we get: 6x^2 - 4x = 20
Rearranging the equation, we get: 6x^2 - 4x - 20 = 0
Dividing the equation by 2, we simplify it to: 3x^2 - 2x - 10 = 0
We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Using the quadratic formula, the equation becomes: x = (-(-2) ± √((-2)^2 - 4(3)(-10))) / (2 * 3)
Simplifying this equation gives: x = (2 ± √(4 + 120)) / 6
Calculating the square root gives: x = (2 ± √(124)) / 6
Taking the positive square root, we get: x = (2 + √(124)) / 6
Calculating the square root of 124 gives: x = (2 + 11.14) / 6
Simplifying this equation gives: x = 13.14 / 6
Dividing gives: x ≈ 2.19
Therefore, the width of the rectangle is approximately 2.19 inches.
The length of the rectangle is 6x - 4 = 6(2.19) - 4 = 13.14 - 4 = 9.14 inches.
Therefore, the length of the rectangle is approximately 9.14 inches. Answer: \boxed{2.19, 9.14}.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99