Question 1160635

The perimeter of the rhombus is 20dm and one of its longer diagonal is 8dm:calculate the length of its shorter diagonal and its area.
<pre>Diagonals of a rhombus are PERPENDICULAR to each other.
As the rhombus' perimeter is 20 dm, each side = {{{matrix(1,4, 20/4, "=", 5, dm)}}}
A rhombus contains 4 right-triangles.
As the longer diagonal's length is 8 dm, and the diagonals of a rhombus bisect each other then each longer leg/side of each right-triangle = {{{matrix(1,4, 8/2, "=", 4, dm)}}}
Wee now have 4 right-triangles with 3-4-5 PYTHAG. TRIPLES, which means that each SHORTER side/leg of each right-triangle = 3, thus making the {{{highlight_green(matrix(1,6, Shorter, "diagonal:", 2(3), "=", 6, dm))}}}
With each of the 4 right-triangles having legs of 3 dm and 4 dm, each right-triangle's area = {{{matrix(1,6, (1/2) * 3(4), "=", (1/2)12, "=", 6, dm)}}}
As there are 4 right-triangles, {{{highlight_green(matrix(1,8, Area, of, rhombus, "=", 4(6), "=", 24, dm^2))}}}