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Question
If perimeter of a rhombus is 100 cm and length of one diagonal is 48 cm, what is the area of the quadrilateral?
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Solution
Perimeter of the rhombus = 100 cm
⇒ `4 xx` side = 100
⇒ side = `100/4` = 25 cm
Thus, each side of the rhombus = 25 cm.
Diagonals of a rhombus are perpandicular bisector of each other.
So, AO = OC = `48/2` = 24 cm
In Δ AOB,
We apply Pythagoras theorem,
AO² + OB² = AB²
⇒ 24² + OB² = 25²
⇒ OB² = 625 - 576 = 49
⇒ OB = 7 cm
So, DB = `2 xx "OB" = 2 xx 7` = 14 cm
Area of rhombus = `1/2 xx` (product of diagonal)
= `1/2 xx 14 xx 48`
= 336 cm²
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