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Question
The diagonals of a rhombus are 18 cm and 24 cm. Find:
(i) its area ;
(ii) length of its sides.
(iii) its perimeter
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Solution
The diagonal of the rhombus is 18 cm and 24 cm.
area of rhombus = `1/2` x Product of diagonals
= `1/2` x 18 x 24
= 216 cm2
(ii)
Diagonals of a rhombus bisect each other at right angles.
∴ OA = `1/2 xx 24 = 12` cm
OB = `1/2 xx 18 = 9` cm
In right ∠d Δ AOB
AB = `sqrt("OA"^2 + "OB"^2)`
= `sqrt((12)^2 + (9)^2)`
= `sqrt(144 + 81)`
= `sqrt(225) = 15` cm
∴ Side of rhombus = 15 cm
(iii)
Perimeter of rhombus = `4 xx "side"`
= `4 xx 15 = 60` cm
(i) 216 cm2 (ii) 15 cm (iii) 60 cm.
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