My geometry is a little rusty due to not doing it for so long. I am trying to find the side of a rectangle by only knowing one sides length. Is this possible?
Length of one side is $0.21875$. I have gone about this using trig by dividing the rectangle into half creating two right angle triangles with theta thus equaling 45 degrees.
Is this the correct way of going about this?
Answers I get are:
$0.1350496052$ (Taking $0.21875$ as Opposite angle)
and
$0.354332582$ (Taking $0.21875$ as Adjacent angle)
Calculations:
$\tan(45) = \frac OA$
Thanks
Best Answer
As pointed out by Gordon, when a rectangle is divided into two parts of equal area through a long diagonal, the angles would not be $45^{\circ}$
Construct a rectangle $ABCD$ and draw $BD.$ Now $\angle ABD=\angle BDC$ as they are alternate angles. If we assume (as you said) that $\angle ABD=\angle DBC=45^{\circ}$ then $\angle BDC$ must also be $45^{\circ}$ but then $\triangle BCD$ will become isosceles meaning $BC=DC$ but it cannot be true as in a rectangle length$\ne$breadth. So we proved that $\angle DBC$ is not $45^{\circ}$ hence we proved that diagonal does not divide $\angle B$ equally.
For your main question, we can't determine the breadth of a rectangle if we just know it's length. The information is insufficient.