how do I find the length and width of a rectangle when the width of the rectangle is 3 feet less tahn the length. The area is 18ft^2
Here is how to get the answer using algebra.
L*W = L*(L-3) = 18
L^2 -3L -18 = 0
(L+3)(L-6) = 0
L = 6 or -3
Take the positive root for L. A negative length does not make sense in this case.
Then compute W.
what is an expression for an area of an equilateral triangle,A, as a function of its diameter,d?
To find the length and width of a rectangle, we can use the given information about the relationship between the width and length, as well as the area of the rectangle.
Let's denote the length of the rectangle as "L" and the width as "W".
From the given information, we know that the width is 3 feet less than the length:
W = L - 3
We also know that the area of a rectangle is given by the formula:
Area = Length * Width
In this case, the area of the rectangle is 18ft^2:
18 = L * W
Now, substitute the value of W from the first equation into the second equation:
18 = L * (L - 3)
Expand and rearrange the equation:
18 = L^2 - 3L
Rearrange the equation into a quadratic form by subtracting 18 from both sides:
L^2 - 3L - 18 = 0
Now we have a quadratic equation in standard form. To solve for L, we can factor the equation or use the quadratic formula.
Factoring the equation:
(L - 6)(L + 3) = 0
Set each factor equal to zero and solve for L:
L - 6 = 0 or L + 3 = 0
If L - 6 = 0, then L = 6.
If L + 3 = 0, then L = -3. However, the length of a rectangle cannot be negative, so we ignore this solution.
Now, substitute the value of L back into the equation W = L - 3 to find the width:
W = 6 - 3
W = 3
Therefore, the length of the rectangle is 6 feet and the width is 3 feet.