the area of a rectangular table =82 square feet if its length is 8 feet longer than its width find the dimensions of the table
L = W + 8
L * W = 82
(W+8)W = 82
W^2 + 8W - 82 = 0
I don't see how this could be factored. Do you have typos?
it has roots with sq. roots not simple integer coz its determinant is not a perfect sq.
piyush has confused the word determinant with discriminant, but is correct in saying thwe roots will not be integers
To find the dimensions of the table, we need to solve a system of equations based on the given information.
Let's define the width of the table as x and the length as x + 8 (since the length is 8 feet longer than the width).
Step 1: Set up the equation for the area of a rectangle.
The formula for the area of a rectangle is given by: Area = length × width.
Since we are given that the area is 82 square feet, we can write the equation as:
82 = (x + 8) × x
Step 2: Simplify the equation.
Multiply x by x + 8:
82 = x^2 + 8x
Step 3: Rearrange the equation.
Move 82 to the other side of the equation:
x^2 + 8x - 82 = 0
Step 4: Solve the quadratic equation.
To solve the equation, we can factor it or use the quadratic formula. Since the equation doesn't easily factor, we'll use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = 8, and c = -82:
x = (-8 ± √(8^2 - 4(1)(-82))) / (2(1))
Simplifying further:
x = (-8 ± √(64 + 328)) / 2
x = (-8 ± √392) / 2
x = (-8 ± 19.8) / 2
x = (-8 + 19.8) / 2 or x = (-8 - 19.8) / 2
x = 11.8 / 2 or x = -27.8 / 2
x = 5.9 or x = -13.9
Since we can't have a negative length or width, we discard the negative solution.
Step 5: Calculate the length.
The width is x = 5.9 feet, and the length is x + 8 = 5.9 + 8 = 13.9 feet.
Therefore, the dimensions of the table are: width = 5.9 feet and length = 13.9 feet.