A rectangular patio has a length of f(x)=4x-3 and a width of g(x)=x-4. If the patio's perimeter was 84 feet, what would the value of x be? Please explain!!
Come on. My math exam is tomorrow.
HELP!!!!!!
length = 4x-3
Width = x-4
2W + 2L = perimeter
2(4x-3) + 2(x-4) = 84
8x - 6 + 2x - 8 = 84
10x = 98
x = 9.8
To find the value of x, you need to set up an equation based on the given information.
The formula for calculating the perimeter of a rectangle is given by P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
In this case, the length of the patio is given by f(x) = 4x - 3 and the width is given by g(x) = x - 4. Since the perimeter of the patio is given as 84 feet, we can set up the equation:
84 = 2(4x - 3) + 2(x - 4)
Now, let's simplify the equation by distributing and combining like terms:
84 = 8x - 6 + 2x - 8
Combining like terms:
84 = 10x - 14
Next, let's isolate the variable x by moving the constant term to the other side of the equation:
10x = 84 + 14
10x = 98
Finally, solve for x by dividing both sides of the equation by 10:
x = 98 / 10
Simplifying, we get:
x = 9.8
Therefore, the value of x is 9.8.