Square of 96 by division method
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Answer:
Lenghts of the sides:
Lenghts of the diagonals: and
Step-by-step explanation:
Look at the rhombus ABCD shown attached, where AC and BD de diagonals of the rhombus.
The sides of a rhombus have equal lenght. Then, since the perimeter of this one is 104 centimeters, you can find the lenght of each side as following:
You know that the diagonals are in the ratio
Then, let the diagonal AC be:
This means that AE is:
And let the diagonal BD be:
So BE is:
Since the diagonals of a rhombus are perpendicular to each other, four right triangles are formed, so you can use the Pythagorean Theorem:
Where "a" is the hypotenuse and "b" and "c" are the legs.
In this case, you can choose the triangle ABE. Then:
Substituting values and solving for "x", you get:
Therefore, the lenghts of the diagonals are:
