Respuesta :
There is an infinite number of length-width pairs that will result in a diagonal value of c.
Let a = the length. This is unknown.
Let b = the width. This is unknown.
Let c = the diagonal. This is a known value.
We have a right triangle with side a, side b, and hypotenuse c.
Since this is a right triangle, we will use the Pythagorean Theorem.
What is the Pythagoras theorem?
The Pythagorean Theorem is
[tex]c^2 = a^2 + b^2.[/tex]
Rearranging this formula gives
[tex]a^2 = c^2 - b^2[/tex]
And,[tex]a = \sqrt{(c^2 - b^2)}[/tex]
Now, if you chose a value for the width, b, then you can compute the corresponding for the length, b, since c is a known value. If you chose another value for the width, you can compute the length value corresponding to your width value.
There is an infinite number of length-width pairs that will result in a diagonal value of c.
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