In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m 2 . Find the length and breadth of the pond.
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x—breadth of the grass:
(50 - 2x)(40 - 2x) = 50(40) - 1,184
2,000 - 100x - 80x + 4x² = 2,000 - 1,184
4x² - 180x = - 1,184
x² - 22.5x = - 296 + (- 22.5)²
x² - 22.5x = - 296 + 506.25
(x - 22.5)² = 210.25
x - 22.5 = ± 14.5 (select the negative 14.5 over the positive 14.5)
x = - 14.5 + 22.5
x = 8
Length of the pond:
= 50 - 2(8)
= 50 - 16
= 34
Width of the pond:
= 40 - 2(8)
= 40 - 16
= 24
Length =34 meters
breadth= 24 meters
(50 - 2x)(40 - 2x) = 50(40) - 1,184
2,000 - 100x - 80x + 4x² = 2,000 - 1,184
4x² - 180x = - 1,184
x² - 22.5x = - 296 + (- 22.5)²
x² - 22.5x = - 296 + 506.25
(x - 22.5)² = 210.25
x - 22.5 = ± 14.5 (select the negative 14.5 over the positive 14.5)
x = - 14.5 + 22.5
x = 8
Length of the pond:
= 50 - 2(8)
= 50 - 16
= 34
Width of the pond:
= 40 - 2(8)
= 40 - 16
= 24
Length =34 meters
breadth= 24 meters
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