Question

perimeter of rhombus is 146 CM one of its diagonal is 55 cm find the area and other diagonal of the Rhombus

Answer 1

Perimeter of rhombus = 146

4× side = 146

Side = 146/4

side = 36.5
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As we know that the diagonals of rhombus bisects each other at 90°

By Pythagoras theorem,

(55/2)² +(half of other diagonal)²=(36.5)²

(27.5)² +(half of other diagonal)²=(36.5)²

(half of other diagonal)²= (36.5)²-(27.5)²

(Half of other diagonal)²= (36.5-27.5)(36.5+27.5)

(half of other diagonal)²= (9)(64)

half of other diagonal =√(9×64)

half of other diagonal = 3×8=24


Other diagonal = 2×24=48

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Area of rhombus = product of diagonal/2

Area of rhombus = 55×48/2

Area of rhombus =55×24 = 1320 cm²

I hope this will help you
-by ABHAY

Answer 2

The diagonal of the rhombus is 36.5 cm.