Answer:
Explanation:
7a - The perimeter of the fence is the sum of the whole path around the fence (2 * length + 2 * width). In this question, L = x+4, and w = 2x - 23 so the perimeter is
2L + 2w
= 2(x+4) + 2(2x-23) distribute the terms through the parentheses
= 2x + 8 + 4x - 46 combine like terms
= 6x - 38
7b - The area is equal to length * width
L * w
= (x+4) * (2x-23) foil the terms
= (x * 2x) + (x * -23) + (4 * 2x) + (4 * -23)
= 2x^2 - 23x + 8x - 92 combine like terms
= 2x^2 - 15x - 92
7c - The equation for the perimeter in part a is 6x - 38, and it is given in part c that the fence is 76 feet, so solve for x
6x - 38 = 76 set equations equal to each other
6x = 114
x = 19
now that we know x, we can plug x into the length and width equations that were given
length = x + 4 = 19 + 4 = 23
width = 2x - 23 = 2 * 19 - 23 = 38 - 23 = 15
so length = 23 feet and width = 15 feet
7d - In part b we created an equation for area, and in part c we figured out the value of x. so to find the area, plug x into the equation from part c
area = 2x^2 - 15x - 92
x = 19
area = 2*(19)^2 - (15* 19) - 92 = 722 - 285 - 92 = 345
so area = 345 feet^2