Applying the Pythagorean theorem, the dimensions of the rectangular plot of land are:
Width of the rectangular plot of land = 16 m
Length of the rectangular plot of land = 30 m
Let x be used to represent the width of the rectangular plot of land.
The dimensions of the rectangular plot of land would be expressed as follows:
Width of the rectangular plot of land = x
Length of the rectangular plot of land = x + 14
Diagonal = 34 m
Use the Pythagorean theorem to form an equation involving the dimensions of the rectangular plot of land:
x² + (x + 14)² = 34²
x² + x² + 28x + 196 = 1156
2x² + 28x + 196 - 1156 = 0
2x² + 28x - 960 = 0
Factorize
(x - 16)(x + 30) = 0
x = 16 or x = -30
Thus, the dimensions of the rectangular plot of land would be:
Width of the rectangular plot of land = x = 16 m
Length of the rectangular plot of land = x + 14 = 16 + 14 = 30 m
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