A big beach towel has a width that is 3 feet less then it's length. If the towel's area 28 square feet, what is it's length?
L = length
w = L - 3
A = Lw
28 = L * (L - 3)
28 = L^2 - 3L
L^2 - 3L - 28 = 0
solve by completing the square
if you are right
L = -4, L = 7
since length can't be neg., throw out -4, so L = 7 and width = 4
This was super helpful! Thank you!
Ah, the mystery of the big beach towel! Let's solve it with some humor, shall we?
Well, let's call the length of this elusive towel "L". According to our information, the width would then be L - 3. Now, since the area is given as 28 square feet, we can set up an equation:
L * (L - 3) = 28
Now, it's time for some mathematical magic! Let's simplify this equation:
L^2 - 3L = 28
Moving all the terms to one side:
L^2 - 3L - 28 = 0
Now, let me summon my imaginary comedy calculator to solve this quadratic equation for us. *puff* *puff* Ah, here it is! According to my calculations, the length of the towel should be...
L = 7 feet!
So, the big beach towel has a length of 7 feet. Now you can relax and imagine all the fun you'll have on that towel. Enjoy, my friend!
Let's denote the length of the towel as "x" feet. According to the given information, the width is 3 feet less than the length, so the width can be expressed as "x - 3" feet.
To find the area of the towel, we multiply the length by the width:
Area = Length * Width
Given that the area is 28 square feet, we can set up the equation as:
28 = x * (x - 3)
Now let's solve this equation to find the length of the towel:
28 = x^2 - 3x
Rearranging the equation:
x^2 - 3x - 28 = 0
This is a quadratic equation that can be factored or solved using the quadratic formula. Factoring may not be straightforward, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In our quadratic equation, "a" is the coefficient of x^2 (which is 1), "b" is the coefficient of x (which is -3), and "c" is the constant term (which is -28). Substituting these values into the quadratic formula, we get:
x = (-(-3) ± √((-3)^2 - 4 * 1 * (-28))) / (2 * 1)
Simplifying:
x = (3 ± √(9 + 112)) / 2
x = (3 ± √121) / 2
x = (3 ± 11) / 2
Solving for both possibilities:
x1 = (3 + 11) / 2 = 14 / 2 = 7
x2 = (3 - 11) / 2 = -8 / 2 = -4
Since length cannot be negative, the length of the towel is 7 feet.
To solve this problem, we can set up an equation based on the given information.
Let's assume that the length of the big beach towel is 'x' feet.
According to the problem, the width of the towel is 3 feet less than its length. So, the width can be represented as 'x - 3' feet.
The area of the towel can be calculated by multiplying the length and width. In this case, the area is given as 28 square feet. So, we have the equation:
Length * Width = Area
x * (x - 3) = 28
Now, we can solve this quadratic equation to find the value of 'x', which represents the length of the towel.
x^2 - 3x = 28
Rearranging the equation:
x^2 - 3x - 28 = 0
To solve this quadratic equation, we can either factorize it or use the quadratic formula. In this case, factoring might be easier.
The factors of -28 that add up to -3 are -7 and 4. So, we can factorize the equation as follows:
(x - 7)(x + 4) = 0
Setting each factor equal to zero:
(x - 7) = 0 or (x + 4) = 0
Solving for 'x' in each case:
x = 7 or x = -4
Since the length of the towel cannot be negative, we can discard the solution x = -4.
Therefore, the length of the big beach towel is 7 feet.