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Question
The perimeter of a rhombus is 40 cm. If one diagonal is 16 cm; find:
- It's other diagonal
- area
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Solution
(i)
Perimeter of rhombus = 40 cm
Perimeter of rhombus = 4 × side
4 × side = 40
side = `40/4 = 10` cm
One diagonal = 16 cm
Diagonals of a rhombus bisect each other at right angles.
OB = `sqrt("AB"^2 - "OA"^2)`
= `sqrt((10)^2 - (8)^2)`
= `sqrt(100 - 64)`
= `sqrt(36)`
= 6 cm
∴ diagonal BD = `6 xx 2 = 12` cm
(ii)
Area of rhombus = `1/2 xx "product of diagonals"`
= `1/2 xx 12 xx 16`
= 96 cm2
∴ (i) 12 cm (ii) 96 cm2
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