Question

The perimeter of a rhombus is 164 cm. If the length of one of the diagonals is 18 cm, find the length other diagonal. Hence, find the area of the rhombus.?
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Answer 1

Answer:

Given that perimeter of the rhombus=164cm

as all the sides of a rhombus are equal in length,

length of a side =164/4 cm=41cm

we know that the two diagonals of a rhombus bisect each other at right angles,

hence, we obtain a right angled triangle.

by Pythagoras theorem,

41²=(18/2)²+( 1/2 length of the other diagonal)²

=>1681=81+ (d/2)² [ d =length of the other diagonal]

=>1681-81=(d/2)²

=>√1600=d/2

=>40=d/2

=>40×2=d

=> d=80cm

here we get the length of the other diagonal is 80cm.

now, area of the rhombus

= 1/2(product of the length of the two diagonals)

=1/2(18×80)

=1440/2

=720cm²

hope it helps :)