Answer:
L = 37 yards and B = 76 yards
L = 38 yards and B = 76 yards
Step-by-step explanation:
Given:
Total length of the fence(perimeter) = 150 yards
One side is fenced using the back side of the house
So, we have
Perimeter of the fence = 2L + W
150 = 2L + W (1)
The fenced-in portion = 2,812 square yards
Area of a rectangle = L × W
2812 = L × W (2)
From (1)
150 = 2L + W
W = 150 - 2L
Substitute W = 150 - 2L into (2)
2,812 = L × W (2)
2,812 = L × (150 - 2L)
2,812 = 150L - 2L²
-2L² + 150L - 2812 = 0
2L² - 150L + 2812 = 0
Divide through by 2
L² - 75L + 1406 = 0
Solve the quadratic equation using factorization method
Find the factors
L² - 37L - 38L + 1406 = 0
L ( L - 37 ) - 38 ( L - 37 ) = 0
( L - 37 ) ( L -38 ) = 0
L - 37 = 0 or L - 38 = 0
L = 37 yards or L = 38 yards
If L = 37 yards
B = 150 - 2L
B = 150 - (2 × 37)
= 150 - 74
= 76 yards
If L = 38 yards
B = 150 - 2L
B = 150 - (2 × 38)
= 150 - 76
= 74 yards
Therefore,
The dimensions of the fence can either be
L = 37 yards and B = 76 yards
L = 38 yards and B = 76 yards
