SOLUTION: True or False.
The sum of the lengths of the diagonals of a rhombus is less than its perimeter.
Algebra.Com
Question 18607: True or False.
The sum of the lengths of the diagonals of a rhombus is less than its perimeter.
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
cosider rhombus ABCD..we have AB=BC=CD=DA=x say..diagonals are AC and BD.consider triangle ABC..as per the property of triangles sum of any 2 sides is more than the third side..so
AB+BC>AC..or 2x>AC
similarly in triangle BCD,we have BC+CD>BD...or..2x>BD
adding these 2 eqns...we have 2x+2x>AC+BD..or..4x>AC+BD
so perimeter is more than sum of diagonals..or sum of diagonals is less than perimeter....TRUE
RELATED QUESTIONS
True or False: The sum of the lengths of the diagonals of a rhombus is less than its... (answered by edjones)
The lengths of the diagonals of a rhombus are 20 and 48 meters. What is the... (answered by ikleyn)
The diagonals of a rhombus differ by 4. If its perimeter is 40, find its... (answered by KMST)
The lengths of the diagonals of a rhombus are 18 cm and 24 cm. What is its perimeter and... (answered by ikleyn)
The diagonals of a rhombus differ by 4. If the perimeter is 40, find its... (answered by ValorousDawn)
The Diagonals of Rhombus measure 16cm and 30cm.Find its... (answered by Edwin McCravy)
The diagonals of a rhombus are of lengths 10 and 24. What is ots perimeter? Please help. (answered by rothauserc)
The lengths of diagonals of a rhombus are in the ratio 2:1. If the perimeter of the... (answered by ankor@dixie-net.com)
a rhombus has sides of length 10 inches, and the lengths of its diagonals difference by 4 (answered by CharlesG2)