The length of a table is 4m longer than the width. The are is 77m^2. Find the dimensions of the table.
l=w+4
w=l-4?
I'm stuck?
As you noted,
l = w+4
Now you only have one more piece of data: the area
a = lw = (w+4)w so,
w^2+4w = 77
w^2+4w-77 = 0
(w+11)(w-7) = 0
w = 7 or -11
Even before working on the algebra, you could have asked yourself, "Self, what are the factors of 77?" 7 and 11.
Hmmm. One is 4 more than the other.
Don't worry, I'm here to help! Let's solve this problem step by step.
We know that the area of the table is 77m², and we also know that the length of the table is 4m longer than the width. So, we can write two equations based on these pieces of information:
1) Area equation: length × width = 77m²
2) Length equation: length = width + 4m
Now, let's substitute the length equation into the area equation:
(width + 4m) × width = 77m²
Expanding this equation, we get:
width² + 4m × width - 77m² = 0
Now, we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± sqrt(b² - 4ac)) / (2a)
In this case, our equation is width² + 4m × width - 77m² = 0, which matches the form ax² + bx + c = 0. We can identify a = 1, b = 4m, and c = -77m². Plugging these values into the quadratic formula, we get:
width = (-4m ± sqrt((4m)² - 4×1×(-77m²))) / (2×1)
width = (-4m ± sqrt(16m² + 308m²)) / 2
width = (-4m ± sqrt(324m²)) / 2
width = (-4m ± 18m) / 2
Now, we have two possible values for the width:
1) width = (-4m + 18m) / 2 = 14m / 2 = 7m
2) width = (-4m - 18m) / 2 = -22m / 2 = -11m
Since width can't be negative in this context, we discard the second solution.
Now that we have the value for the width (7m), we can substitute it into the length equation:
length = width + 4m = 7m + 4m = 11m
So, the dimensions of the table are 7m (width) and 11m (length).
I hope this helps! Let me know if you have any other questions.
To find the dimensions of the table, we can use the given information that the area is 77m².
Let's assume the width of the table is "w" meters.
From the problem statement, we know that the length of the table is 4 meters longer than the width. So, the length can be expressed as "w + 4" meters.
Now, we can set up the equation for the area of the table:
Area = Length × Width
77m² = (w + 4)m × wm
77m² = w² + 4w
Rearranging the equation, we get a quadratic equation:
w² + 4w - 77 = 0
Now, we can solve this quadratic equation to find the width (w) of the table using factoring, completing the square, or the quadratic formula.
Factoring:
(w - 7)(w + 11) = 0
By setting each factor equal to zero and solving for w, we get two possible values:
w - 7 = 0 or w + 11 = 0
w = 7 or w = -11
Since the width cannot be negative, we discard w = -11.
Therefore, the width of the table is 7 meters.
Now, we can find the length of the table as:
Length = Width + 4
Length = 7 + 4
Length = 11 meters
So, the dimensions of the table are:
Width = 7 meters
Length = 11 meters
To find the dimensions of the table, we can set up an equation based on the given information.
Let's assume the width of the table is represented by the variable 'w.' According to the problem, the length is 4 meters longer than the width, so the length can be represented by 'w + 4'.
The area of a rectangle is calculated by multiplying the length by the width. In this case, we know that the area is 77 square meters. So we have the equation:
w * (w + 4) = 77
To solve for the dimensions, we need to solve this quadratic equation. We can start by expanding the equation:
w^2 + 4w = 77
Rearranging the equation in the standard form:
w^2 + 4w - 77 = 0
Now we have a quadratic equation. Since it is not easily factorable, we can use the quadratic formula to find the values of 'w':
w = (-b ± √(b^2 - 4ac)) / 2a
For our equation, a = 1, b = 4, and c = -77. Substituting these values into the formula:
w = (-4 ± √(4^2 - 4(1)(-77))) / 2(1)
Simplifying the expression within the square root:
w = (-4 ± √(16 + 308)) / 2
w = (-4 ± √324) / 2
w = (-4 ± 18) / 2
Now we have two possible solutions for 'w':
1) w = (-4 + 18) / 2 = 14 / 2 = 7
2) w = (-4 - 18) / 2 = -22 / 2 = -11
Since the width of an object cannot be negative, we discard the second solution.
Therefore, the width of the table is 7 meters.
To find the length, we can substitute the value of 'w' back into the equation for the length:
l = w + 4
l = 7 + 4
l = 11
So, the dimensions of the table are 7 meters width and 11 meters length.