Henry
answered
Eq2: 2L + 2W = 84Ft.
L + W = 42.
L e 42-W,
In Eq1, substitute 42-W for L:
(42-W)W = 425,
42W - W^2 - 425 = 0,
W^2 -42W + 425 = o,
(W-25)(W-17) = 0,
W-25 = 0,
W = 25.
W-17 = 0,
W = 17.
In Eq1 substitute 17 for W:
L*17 = 425,
L = 25 Ft., W = 17.
When L = 17, W = 25.
Explain Bot
answered
Let's assume that the length of the rectangle is L and the width is W.
We know that the area of a rectangle is given by the formula: Area = Length * Width
In this case, the area of the rectangle is given as 425 square feet, so we can write the equation as:
L * W = 425 ----(Equation 1)
We also know that the perimeter of the rectangle is given by the formula: Perimeter = 2 * (Length + Width)
In this case, the perimeter is given as 84 feet, so we can write the equation as:
2 * (L + W) = 84 ----(Equation 2)
Now, we have a system of equations with two variables (L and W). We can solve this system to find the values of L and W that satisfy both equations.
To solve the system, we can use substitution or elimination method. Let's use substitution method:
From Equation 1, we can solve for L in terms of W:
L = 425 / W
Now, substitute this value of L into Equation 2:
2 * (425 / W + W) = 84
Simplify the equation:
2 * (425 + W^2) / W = 84
Multiply both sides of the equation by W to eliminate the denominator:
2 * (425 + W^2) = 84 * W
Expand and rearrange the equation:
850 + 2W^2 = 84W
Rearrange the equation in standard quadratic form:
2W^2 - 84W + 850 = 0
Now, we can solve this quadratic equation for W.
You can use the quadratic formula: W = (-b +/- sqrt(b^2 - 4ac)) / 2a
In this case, a = 2, b = -84, and c = 850.
Substitute these values in the quadratic formula to find the values of W. Once you have the value of W, substitute it back into Equation 1 to find the value of L.
Finally, you will have the length (L) and width (W) of the rectangle.
