The length of a rectangle is 4cm more than its width. If the area of the rectangle is 117cm^2, what is the length?
So : 117cm^2= (w)(w+4)
= w^2 + 4w
I don't know what to do next
w^2 + 4 w - 117 = 0
Do you know how to use the quadratic equation?
w = [ -4 +/- sqrt (16 + 468) ] /2
w = -2 +/- (1/2) sqrt 484 )
w = -2 +/- (1/2)22
w = -2 +/- 11
use the + root
w = 9
then L = 13
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check
9 * 13 = 117 sure enough
Or now that I know the answer:
w^2 + 4 w - 117 = 0
(w-9)(w+13) = 0
To solve the equation w^2 + 4w = 117, you can rearrange the equation to get a quadratic equation, even if it doesn't appear to be in standard quadratic form.
1. Start with the equation: w^2 + 4w = 117.
2. Rearrange the equation by moving all the terms to one side: w^2 + 4w - 117 = 0.
Now, you can solve the equation in two ways:
A) Factoring
B) Using the quadratic formula
A) Factoring:
In this case, the equation w^2 + 4w - 117 = 0 cannot be easily factored, so let's move on to the quadratic formula.
B) Quadratic Formula:
The quadratic formula is given by: w = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are coefficients of the equation in the form ax^2 + bx + c = 0.
In our case, a = 1, b = 4, and c = -117. Plugging these values into the quadratic formula, we get:
w = (-4 ± √(4^2 - 4 * 1 * -117)) / (2 * 1)
Simplifying further:
w = (-4 ± √(16 + 468)) / 2
w = (-4 ± √484) / 2
w = (-4 ± 22) / 2
w = (18 / 2) or (-26 / 2)
Therefore, we have two possible solutions for w: w = 9 or w = -13.
Since the width cannot be negative, we discard the negative solution.
So, the width of the rectangle is 9 cm.
Now, since the length is 4 cm more than the width, the length of the rectangle is 9 + 4 = 13 cm.
Hence, the length of the rectangle is 13 cm.