The area of a rhombus is 28cmsquare. one of it's diagonal is 4cm.find the perimeter.

Asked by sakkhogun24 | 26th Nov, 2014, 09:45: PM

Expert Answer:

W e space k n o w space t h a t space A r e a space o f space a space r h o m b u s equals 1 half cross times d subscript 1 cross times d subscript 2 G i v e n space t h a t space A r e a space o f space t h e space r h o m b u s equals 28 space c m squared space a n d space d subscript 1 equals 4 space c m T h u s comma space w e space h a v e comma 28 equals 1 half cross times 4 cross times d subscript 2 rightwards double arrow 28 cross times 2 equals 4 cross times d subscript 2 rightwards double arrow fraction numerator 28 cross times 2 over denominator 4 end fraction equals d subscript 2 rightwards double arrow d subscript 2 equals 14 D i a g o n a l s space o f space t h e space r h o m b u s space b i s e c t space p e r p e n d i c u l a r l y space e a c h space o t h e r. T h e r e f o r e space a p p l y i n g space P y t h a g o r a s space T h e o r e m comma space w e space h a v e comma s i d e squared equals open parentheses d subscript 1 over 2 close parentheses squared plus open parentheses d subscript 2 over 2 close parentheses squared rightwards double arrow s i d e squared equals open parentheses 4 over 2 close parentheses squared plus open parentheses 14 over 2 close parentheses squared rightwards double arrow s i d e squared equals open parentheses 2 close parentheses squared plus open parentheses 7 close parentheses squared rightwards double arrow s i d e squared equals 4 plus 49 rightwards double arrow s i d e squared equals 53 rightwards double arrow s i d e equals square root of 53 P e r i m e t e r equals 4 cross times s i d e rightwards double arrow P e r i m e t e r equals 4 cross times square root of 53

Answered by Vimala Ramamurthy | 27th Nov, 2014, 10:12: AM