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a) The sides of a rhombus are all congruent. (the same length).
⇒AB=BC=CD=DA
b) The two diagonals are perpendicular, and they bisect each other. This means they cut each other in half.
⇒AO=OC=12AC,andBO=OD=12BD
Given that the two diagonals are 30,and16,
⇒AO=302=15,BO=162=8,∠AOB=90∘
From Pythagorean theorem, we know
AB2=AO2+BO2
⇒AB=√152+82=√289=17
SInce AB=BC=CD=DA,
perimeter of ABCD=17⋅4=68
⇒AB=BC=CD=DA
b) The two diagonals are perpendicular, and they bisect each other. This means they cut each other in half.
⇒AO=OC=12AC,andBO=OD=12BD
Given that the two diagonals are 30,and16,
⇒AO=302=15,BO=162=8,∠AOB=90∘
From Pythagorean theorem, we know
AB2=AO2+BO2
⇒AB=√152+82=√289=17
SInce AB=BC=CD=DA,
perimeter of ABCD=17⋅4=68
sa545:
nice answer
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