to 1.) A rectangle is divided into 2 congruent right triangles by one diagonal. The diagonal is the hypotenuse of the right triangle. If l is the length of the rectangle, w is the width and d is the diagonal then you have the equation:
. Plug in the values you know:
and solve for w. (1)
to 2.) A square is a special rectangle with l = w. Use the formula given above and solve for l:
to 3.) A rhombus is divided by the 2 diagonals into 4 congruent right triangles where the side of the rhombus is the hypotenuse.
length of one side: 10
half of the given diagonal: 6
If the half of the other diagonal is e (in Germany usually the diagonals are labeled e and f) then you get:
. Solve for e and calculate the complete length. (16)
to 3.) again: If s is the length of one side of the square then the perimeter of a square is . Calcualte the length of one side (same procedure as in #2.) and then the perimeter.
to 4.) An equilateral triangle is divided into 2 congruent right triangles where the side of the triangle is the hypotenuse, one leg is the altitude and the other leg is the half of one side. Let h be the altitude then you have:
. Solve for h.