The perimeter of rhombus is [tex]60\ cm[/tex] and Distance between the parallel sides is [tex]14.4 \ cm[/tex].
Given,
The lengths of the diagonals of a rhombus are [tex]18cm[/tex] and [tex]24cm[/tex].
Properties of rhombus:
We know that all sides of the rhombus are equal and its diagonal are perpendicularly bisect each other.
So, the rhombus is divided in 4 right triangles whose base is [tex]9 \ cm[/tex] and perpendicular is [tex]12\ cm[/tex] respectively.
On applying the Pythagoras theorem in any one triangle,
[tex](Hypotenuse)^2=(perpendicular)^2+(base)^2[/tex]
[tex](Hypotenuse)^2=(12)^2+(9)^2[/tex]
Or,
[tex](Hypotenuse)^2=144+81[/tex]
[tex](Hypotenuse)^2=225[/tex]
[tex]Hypotenuse=\sqrt{225}[/tex]
[tex]Hypotenuse=15[/tex].
We have, perimeter of rhombus
[tex]P[/tex] [tex]= 4 \times side[/tex]
[tex]perimeter=4\times15[/tex]
[tex]perimeter= 60[/tex][tex]\ cm[/tex].
We know that Area of rhombus,
[tex]A[/tex] [tex]= \frac{1}{2} d_{1} \times d_{2}[/tex].
[tex]A=\frac{1}{2}\times18\times24[/tex]
[tex]A=216 \ cm^2[/tex].
Now, We have another formula for calculating the area of rhombus when we don't have the value of its diagonal in that case,
Area of rhombus will be,
[tex]A= base \times height[/tex]
We have, [tex]A=216[/tex] and [tex]base= 15[/tex]
Putting the above values, we get
[tex]216=15 \times height[/tex]
Or,
[tex]Height= \frac{216}{15}[/tex]
[tex]Height = 14.4 \ cm[/tex].
Hence the perimeter of rhombus is [tex]60\ cm[/tex] and Distance between the parallel sides is [tex]14.4 \ cm[/tex].
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