if perimeter of a rhombus is 100 cl and length of one diagonal is 48 cm, what is the area of the quadrilateral
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If the perimeter of a rhombus is 100 cm, and the length of one diagonal is 48 cm, what is the area of the quadrilateral?
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5 ANSWERS
Ved Prakash Sharma
Ved Prakash Sharma, former Lecturer at Sbm Inter College, Rishikesh (1971-2007)
Answered Jan 9
Length of each side of a rhombus =perimeter/4 = 100 cm/4 = 25 cm.
Let ABCD is a rhombus in which AB=BC=CD=DA=25 cm. and diagonal AC=48
cm. Diagonals AC and BD meet at O. In right angled triangle AOB:-
OB^2+OA^2= AB^2
or. (BD/2)^2+(AC/2)^2 =(25)^2
or. (BD/2)^2+(48/2)^2=625
or. (BD/2)^2=625–576 = 49
or. BD/2= 7 => BD =14 cm.
Area of the quadrilateral (rhombus) =(1/2)×AC×BD=(1/2)×48 cm×14 cm
= 336 cm^2.