abcd is a rhombus whose diagonals intersect at o.if ab=10cm and bd =16cm,find the length of diagonal ac
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In a rhombus diagonals are equal so bd is a diagonals ac=16
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we know in rhombus diagonal bisect each other at right angles
In ∆ AOB
BO= BD/2 =16/2 = 8cm
Using Pythagorous theorems in ∆AOB
AB^2 =AO^2 +BO^2
10^2 = AO ^2+8^2
100-64 =AO^2
AO^2 =36
AO =√36 = 6cm
Therefore length of diagonal AC of rhombus ABCD is 6×2 = 12 cm.
In ∆ AOB
BO= BD/2 =16/2 = 8cm
Using Pythagorous theorems in ∆AOB
AB^2 =AO^2 +BO^2
10^2 = AO ^2+8^2
100-64 =AO^2
AO^2 =36
AO =√36 = 6cm
Therefore length of diagonal AC of rhombus ABCD is 6×2 = 12 cm.
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