length and width of a rectangle
A=198 in
width =x
length =x+7
To find the length and width of a rectangle, you need to use the given information and apply some mathematical steps.
From the given information, we have the equation:
Area (A) = Length × Width
In this case, the given area is 198 in² and we need to find the length and width.
Let's proceed with the calculations:
1. Substitute the given values:
198 in² = (x + 7) in × x in
2. Expand and rearrange the equation:
198 = x² + 7x
3. Convert the equation to standard form:
x² + 7x - 198 = 0
Now we have a quadratic equation which can be solved to find the value of x.
4. Solve for x using factoring, quadratic formula, or other appropriate methods.
Assuming you use the quadratic formula, it states:
x = (-b ± √(b² - 4ac)) / (2a)
In our equation, a = 1, b = 7, and c = -198.
Using the quadratic formula, we can calculate the possible values of x.
x₁ = (-7 + √(7² - 4 × 1 × -198)) / (2 × 1)
x₂ = (-7 - √(7² - 4 × 1 × -198)) / (2 × 1)
Simplifying further:
x₁ = (-7 + √(49 + 792)) / 2
x₂ = (-7 - √(49 + 792)) / 2
x₁ = (-7 + √841) / 2
x₂ = (-7 - √841) / 2
x₁ = (-7 + 29) / 2
x₂ = (-7 - 29) / 2
x₁ = 22 / 2
x₂ = -36 / 2
x₁ = 11
x₂ = -18
Since the dimensions of a rectangle cannot be negative, we discard x₂.
Therefore, the width (x) of the rectangle is 11 inches.
To find the length, we can substitute this value of x into the length formula:
Length = Width + 7
Length = 11 + 7
Length = 18 inches
Therefore, the length of the rectangle is 18 inches and the width is 11 inches.
What are we doing?
Are we finding the value of x?
if so, then ....
x(x+7) = 198
x^2 + 7x - 198 = 0
(x-11)(x+18) = 0
x = 11 or x = -18, but clearly x > 0
so x = 11