Question

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.

Answer 1

Answer:

dimensions are 2.19 inches by 9.14 inches

Step-by-step explanation:

Here, we are interested in knowing the dimensions of the rectangle

Now, let the width of the rectangle be x, from the question, we can write;

6x-4 as the length

Area of rectangle = l * b

x(6x-4) = 20

6x^2 - 4x = 20

divide through by 2

3x^2-2x = 10

3x^2 -2x -10 = 0

using quadratic formula;

x = -b ± √(b^2 - 4ac)/2a

From the quadratic equation, a = 3, b = -2 and c = -10

substituting these values, we have

x = 2 ± √(-2)^2 -4(3)(-10))/6

x = 2 ± √(124)/6

x = 2 + √(124)/6 or 2 - √(124)/6

x = (2+11.14)/6 or (2-11.14)/6

x = 2.19 or -1.52

Since width cannot be negative, we choose 2.19 alone

So the length is 6(2.19) -4 = 9.14