SOLUTION: A floor tile in the shape of rhombus has sides of length 52cm and a diagonal of length 48cm,find 1)the length of the other diagonal 2)the area of the floor tile.

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Question 1205660: A floor tile in the shape of rhombus has sides of length 52cm and a diagonal of length 48cm,find
1)the length of the other diagonal
2)the area of the floor tile.
Answer by ikleyn(52781) About Me  (Show Source):
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A floor tile in the shape of rhombus has sides of length 52 cm and a diagonal of length 48 cm, find
1) the length of the other diagonal
2) the area of the floor tile.
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(1)  The diagonals of a rhombus are perpendicular and bisect each other.


     Therefore, half of the other diagonal is

         x = sqrt%2852%5E2-%2848%2F2%29%5E2%29 = sqrt%2852%5E2-24%5E2%29 = sqrt%282128%29 = 4%2Asqrt%28133%29 = 46.13025  (approximately).


     Hence, the other diagonal is twice this value, or  2x = 8%2Asqrt%28133%29 = 92.2605  cm  (rounded).    ANSWER



(2)  The area of the rhombus is half the product of its diagonals

         area = %281%2F2%29%2A48%2A8%2Asqrt%28133%29 = 192%2Asqrt%28133%29 = 2214.252  cm^2  (rounded).

Solved.