this is what i have left but i don't know how to finish it.
THe length of a rectangle is 1cm more than 4 times its width. if the area of the rectangle is 74cm^2, find the dimensions of the rectangle to the nearest thousandsth.
so then:
a =Lw
A = 74
W= W
L=4W+1
FROM ALL THIS I END UP WITH
0 = 4W^2+W-74
THEN I USED THE QUADRATIC EQUATION
AND I AM IN THIS STEP:
X=(-1 +/- sqrt 1185)/(8) from here is what i don't know .
It's really simple. If you follow thw steps i showed you in your previous question you'll get it. You have the right values, not just do the math.
-1 minus sqrt(1185)/8 and -1 plus sqrt(1185)/8. Obviously your negative answer is the wrong one
i get this:
width : 4.2cm
length: 17.8cm
To find the dimensions of the rectangle, we can solve the quadratic equation you obtained:
0 = 4W^2 + W - 74
Using the quadratic formula:
W = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 4, b = 1, and c = -74. Plugging these values into the formula, we get:
W = (-1 ± √(1^2 - 4(4)(-74))) / (2*4)
Simplifying this further:
W = (-1 ± √(1 + 1184)) / 8
W = (-1 ± √1185) / 8
Now, you correctly identified that the negative answer doesn't make sense in the context of the problem. So, we can discard the negative value and focus on the positive value.
W = (√1185 - 1) / 8
Now we can substitute this value of W into the expression for the length of the rectangle:
L = 4W + 1
L = 4((√1185 - 1) / 8) + 1
L = (√1185 - 1) / 2 + 1
The width of the rectangle is approximately 4.2 cm (rounded to the nearest thousandth) and the length is approximately 17.8 cm (rounded to the nearest thousandth).