EFGH is a rhombus. Given EG = 16 and FH = 12, what is the length of one side of the rhombus?
2 answers:
We can calculate the side length with this formula:
<span>4 • Side² = Long Diagonal² + Short Diagonal²
</span><span>4 • Side² = 16² + 12²
</span><span>4 • Side² = 256 + 144
</span><span>4 • Side² = 400
</span><span>Side² = 100
</span>Side = 10
Source:
http://www.1728.org/quadltrl.htm
<u>Answer</u>
= 10
<u>Explanation</u>
EG is one of the diagonals of the rhombus and the other diagonal is FH.
EG = 16 and FH = 12
The diagonals of a rhombus meet at 90°
From this information we can form a right triangle with legs (16/2)=8 and (12/2)=6
The hypotenuse of this triangle is the side of the rhombus.
Using the pythagorean theorem;
L² = 6²+8²
Where L is the length of the rhombus.
L² = 6²+8²
L = √36+64
= √100
= 10
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