Answer:
C. 30 units. Just took the test and got it right
Answer:
As, it is given that , Area of Parallelogram W X Y Z= 45 square units.
Area of Δ [tex]=\frac{1}{2}absinC[/tex]
As, diagonal of parallelogram divides it into two congruent triangles and congruent triangles have equal area.
So, Area (Δ W Y Z)= Area (Δ W X Y)
Area (Δ W X Z) =Area (Δ X Y Z)
Area (Δ WYZ) [tex]=\frac{1}{2}(WZ)*(ZY)sinZ[/tex]
[tex]WZ*ZY Sin Z=22.5 *2\\\\ WZ* ZY*SinZ=45\\\\ Similarly, WX*XY*SinX=45\\\\ Similarly, WX*WZ*SinW=45\\\\ Similarly, XY*ZY*Sin Y=45[/tex]
As, Opposite sides as well as Opposite angles of Parallelogram are equal.
Adding all the equation written above,
2(WZ*ZY*Sin Z )+ 2(WX*WZ*SinW)=180
2 * WZ *ZY(Sin Z +Sin W)=180
WZ *ZY(Sin Z +Sin W)=90
Consider the case when , SinZ=SinW=1, when the parallelogram turns into rectangle.
Area of Parallelogram which is rectangle =45 square units
L*B=45
Perimeter of Parallelogram = 2 * (L +B)
[tex]P=2 L +2* \frac{45}{L}\\\\ P =2 L + \frac{90}{L}[/tex]
Differentiating Once w.r.t L
[tex]P'=2-\frac{90}{L^2}[/tex]
For maxima or minima
L²=45
L= 6.70 units
Gives, B= 6.72 units
Perimeter = 2 × (L +B)
= 2 × (6.70 +6.72)
=2 × 13.42
= 26.84
As, area of parallelogram is smaller than area of rectangle having same dimension.
So, Approximate perimeter of Parallelogram = 30 units.
Option C: 30 units
