The perimeter of a rectangle is 58.8 km, and its diagonal length is 21 km. Find its length and width
2 answers:
Length: 16.8 or 12.6
Diagonal 21
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.
Answer: 12.6 km by 16.8 km
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