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A diagonal of a rhombus, of which the sides are 52cm, is 48cm. What is the length of the other diagonal?
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Solution 1
Diagonals of a rhombus divide it in four congruent right-angled triangles.
By considering one such a triangle, we know its hypotenuse (52 cm) and one of two legs ( = 24 cm).
Then we can find the other leg as = = 46.13 cm (approximately)
So, 46.13 cm is half of the unknown diagonal and 92.26 cm is the entire diagonal length.
Answer. The length of the other diagonal is about 92.26 cm.
Solution 2
If "a" is the length of the rhombus side and "c" and "d" are the lengths of its diagonals, then
= .
See the lesson The length of diagonals of a rhombus in this site.
Hence, = , where d is the length of the other diagonal.
Then d = = 92.26 cm (approximately).
We have the same answer as in the Solution 1.