Question 1093827
<pre>
The length of the shorter diagonal of a rhombus Is 12cm
. A)given That the erea of the rhombus Is 192cm� .find the length of the longeur side
. B) given That the length of the longer aide Is 2 times than of the shorter .find the erea of the rhombus 
. Please show all step

A rhombus is a parallelogram with all sides CONGRUENT, so THIS question must be about the diagonals.

A) given That the <s>erea</s> area of the rhombus Is 192 cm, find the length of the <s>longeur side</s> longer DIAGONAL

With D<sub>L</sub> and D<sub>S</sub> being lengths of the longer and shorter diagonals, respectively, {{{matrix(1,7, Area, of, rhombus, "=", (1/2), of, (D[L] * D[S]))}}}                                                                                             
                                                                                             {{{matrix(2,3, 192, "=", (1/2)12D[L], 192, "=", 6D[L])}}}
                                                                Length of longer diagonal, or {{{highlight_green(matrix(1,6, D[L], "=", 192/6, "=", 32, cm))}}}

<u><font color = red><font size  = 4><b>R E I T E R A T E D</font></font></b></u>
A rhombus is a parallelogram with all sides CONGRUENT, so THIS question must be about the diagonals.

B) given That the length of the longer <s>aide</s> DIAGONAL Is 2 times <s>than</s> that of the shorter. find the <s>erea</s> area of the rhombus. 

Let shorter DIAGONAL be S
Then longer is 2S 
{{{matrix(1,7, Area, of, rhombus, "=", (1/2), of, (D[L] * D[S]))}}}                                                                                             
                  {{{matrix(3,2, "=", (1/2)(2S * S), "=", (1/2)(2S^2), "=", S^2)}}}

So, <font color = red><font size = 4><b>area of ANY rhombus with its LONGER DIAGONAL twice its SHORTER DIAGONAL</font></font></b> is its<font color = red><font size = 4><b> (SHORTER DIAGONAL)<sup>2</sup>.</font></font></b></pre>