Question

A rectangular plot of land is designed so that its length is 14 meters more than its width. The diagonal of the land is known to be 34 meter. What are the dimensions of the land?

Answers

  1. 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

    How to Apply the Pythagorean Theorem?

    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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