The length of the top of a table is 5 m greater than the width. The area is 104m^2. Find the dimensions of the table
The width of the table is _____m
The length of the table is ____m
w(w+5) = 104
w^2 + 5 w - 104 = 0
w = [ -5 +/- sqrt (25 + 416)] /2
w = [ -5 +/- 21 ]/ 2
w = 8 or w = 13
L = 8+5 = 13 then A = 8*13 = 104
w = 13 is too big
so 8 by 13
w = -13 is the other choice, no good
Let's solve this step-by-step.
Step 1: Assign variables:
Let's call the width of the table "w" in meters.
Since the length is 5 meters greater than the width, we can express the length as "w + 5" meters.
Step 2: Write an equation for the area:
The area of a rectangle is equal to the length multiplied by the width. So we can write the equation:
Area = Length * Width
104m^2 = (w + 5)m * wm
Step 3: Simplify the equation:
Multiply the width and length in the equation:
104m^2 = (w^2 + 5w)m^2
Step 4: Solve the quadratic equation:
The equation is quadratic because there is a square term (w^2).
Let's move all terms to one side and set it equal to zero:
w^2 + 5w - 104 = 0
Step 5: Factor or use the quadratic formula to solve the equation:
This equation does not factor easily, so we'll use the quadratic formula:
w = (-5 ± √(5^2 - 4 * 1 * (-104))) / (2 * 1)
Step 6: Solve for w:
Simplifying the equation inside the square root:
w = (-5 ± √(25 + 416)) / 2
w = (-5 ± √441) / 2
w = (-5 ± 21) / 2
Step 7: Determine the valid value for w:
Since the width cannot be negative, we can disregard the negative solution:
w = (21 - 5) / 2
w = 16 / 2
w = 8
Step 8: Find the length:
The length is 5 meters greater than the width, so:
Length = w + 5
Length = 8 + 5
Length = 13
Therefore, the width of the table is 8 meters and the length is 13 meters.
To find the dimensions of the table, we need to use the information given and solve for the width and length.
Let's start by assigning a variable to represent the width of the table. Let's say the width is "w" meters.
According to the problem, the length of the top of the table is 5 meters greater than the width. So the length can be expressed as "w + 5".
The area of the table is given as 104m^2. The formula for the area of a rectangle is length multiplied by width. In this case, the area is 104m^2, so we can write the equation:
(w + 5) * w = 104
Expanding this equation gives us:
w^2 + 5w = 104
Now, we have a quadratic equation. To solve it, we can rearrange the equation in the standard quadratic form:
w^2 + 5w - 104 = 0
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:
The quadratic formula is:
w = (-b ± √(b^2 - 4ac)) / 2a
For this equation, a = 1, b = 5, and c = -104. Plugging in these values, we get:
w = (-5 ± √(5^2 - 4 * 1 * -104)) / (2 * 1)
Now we simplify the equation inside the square root:
w = (-5 ± √(25 + 416)) / 2
w = (-5 ± √441) / 2
w = (-5 ± 21) / 2
We get two possible values for w:
w = (-5 + 21) / 2 = 8
w = (-5 - 21) / 2 = -13
Since the width cannot be negative, we discard the value w = -13.
Therefore, the width of the table is 8m.
The length of the table is given by the equation w + 5:
Length = 8 + 5 = 13m.
So, the dimensions of the table are:
Width = 8m
Length = 13m