Answer:
Step-by-step explanation:
Area = 192 m²
Perimeter= 56 m
Width = x m
Perimeter = 56
2*(length + width) = 56
Divide the equation by 2
l + x = 56/2
l + x = 28
l = 28 - x
Area = 192 m²
l * w = 192
(28 - x)*x = 192
28x - x*x = 192
0 = 192 - 28x + x²
x² - 28x + 192 = 0
2) Equation is a quadratic equation. The roots of this equation will the dimensions of the rectangular plot.
3) The roots represent the width and length of the rectangle.
x² - 28x +192 = 0
Sum = -28
Product =192
Factors = -16 , -12 {-16 +(-12) = -28 & (-12)*(-16) = 192}
x² - 28x + 192 = 0
x² - 12x - 16x + (-16)*(-12) = 0
x(x -12) - 16(x - 12) = 0
(x - 12)(x -16) =0
x -12 = 0 ; x - 16 = 0
x = 12 ; x = 16
x = 12 ,16
4) Sum of the roots = 12 + 16 = 28
Sum of the roots = half of the perimeter
5) Product of the roots = 12*16 = 192 = area of the rectangle.
