The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
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Let length of shorter side = x m
length of bigger side = (x + 30) m
length of diagonal = (x + 60) m
see figure,
we have to use Pythagoras theorem,
so, diagonal ² = bigger side² + shorter side²
=> (x + 60)² = (x + 30)² + x²
=> x² + 120x + 3600 = x² + 60x + 900 + x²
=> 60x + 2700x = x²
=> x² - 60x - 2700 = 0
=> x² - 90x + 30x - 2700 = 0
=> x(x - 90) + 30(x - 90) = 0
=> x = -30 and 90 but x ≠ -30
hence, length of shorter side = 90m
length of bigger side = 120m
length of bigger side = (x + 30) m
length of diagonal = (x + 60) m
see figure,
we have to use Pythagoras theorem,
so, diagonal ² = bigger side² + shorter side²
=> (x + 60)² = (x + 30)² + x²
=> x² + 120x + 3600 = x² + 60x + 900 + x²
=> 60x + 2700x = x²
=> x² - 60x - 2700 = 0
=> x² - 90x + 30x - 2700 = 0
=> x(x - 90) + 30(x - 90) = 0
=> x = -30 and 90 but x ≠ -30
hence, length of shorter side = 90m
length of bigger side = 120m
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In the attachments I have answered this problem. According to given information equations are formed by connecting length, breadth and diagonal. Length and breadth are found by applying Pythagoras theorem. See the attachment for detailed solution.
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