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The perimeter of a rhombus is 146 cm and one of its diagonals is 55cm. Find the other diagonal and the area of the rombhus.
A) 24 cm, 660 sq. cm
B) 24 cm, 330 sq. cm
C) 48 cm, 660 sq. cm
D) 48 cm, 1320 sq. cm
Asked by pragyagupta03 | 20 Dec, 2014, 12:29: PM
answered-by-expert Expert Answer

Correct Answer: D

Solution: Here perimeter = 146

All sides of a rhombus are equal. Length of each side = begin mathsize 16px style 146 over 4 equals 36.5 space cm end style

Diagonals in a rhombus bisect each other at right angles. O is the midpoint of AC and BD. But BD = 55. thereforeOB = OD =27.5 cm

begin mathsize 16px style For space increment AOB comma angle AOB space equals space 90 degree By space Pythagoras space thm comma AB squared equals AO squared plus OB squared 36.5 squared equals AO squared plus 27.5 squared open parentheses 36.5 squared minus 27.5 squared close parentheses space equals space AO squared open parentheses 36.5 plus 27.5 close parentheses open parentheses 36.5 minus 27.5 close parentheses equals AO squared 64 cross times 9 equals AO squared AO equals 24 Length space of space diagonal space AC space equals space 24 space plus space 24 space equals 48 space cm Also comma Area space of space Rhombus space equals space 1 half cross times straight d subscript 1 cross times straight d subscript 2 space equals space 1 half cross times 48 cross times 55 equals space 24 cross times 55 equals space 1320 space sq. space cm end style




Answered by Mili Hariyani | 30 Nov, 2017, 02:27: PM

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