Question

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Answer 1

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.