Answer:
Width of the rectangle = 6.7 ft
length of the rectangle = 10.7 ft
Step-by-step explanation:
ABCD is the rectangle.
AB = length of the rectangle = 4 + x ft
BC = width of the rectangle = x ft
AC = Diagonal of the rectangular field = 12 ft
Since ΔABC is the Right angle triangle. So
[tex]AC^{2} = AB^{2} + BC^{2}[/tex]
[tex]12^{2} = (4 + x)^{2} + x^{2}[/tex]
[tex]144 = x^{2} + 16 + x^{2} + 8 x[/tex]
[tex]144 = 2x^{2} + 8x + 16[/tex]
[tex]x^{2} + 4x -72 = 0[/tex]
By solving above equation we get
x = 6.7 ft
Thus is the width of the rectangle.
And length of the rectangle = 4 + x
⇒ 4 + 6.7
⇒ 10.7 ft
