The perimeter of a rectangle is 58.8 km, and its diagonal length is 21 km. Find its length and width

Sides x and y

2x + 2y = 58.8

x + y = 29.4

y = 29.4 - x

x² + y² = 21²

x² + (29.4 - x)² = 21²

100x² - (294 - 10x)² = 210²

200x² - 2(2940)x + 294² - 210² = 0

200x² - 2(2940)x + (294-210)(294+210) = 0

200x² - 2(2940)x + (84)(504) = 0

Common factor of 8,

25x² - 735 x + (21)(252) = 0

(5 x - 63) (5 x - 84) = 0

x = 63/5 or x = 84/5

x = 12.6 or x = 16.8

The problem is symmetrical so when one of these is the length the other is the width.

12.6 km by 16.8 km

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