Q3 of 27 Page 289

If the length of one diagonal of a rhombus having the side 10cm. length is 12cm., then let us write, by calculating the length of other diagonal.

Given: Side of rhombus = 10 cm


Length of one diagonal = 12 cm


The figure for the question is:



We know that diagonals a rhombus are perpendicular bisector to each other.


So, the ΔAOB is a right angled triangles with ∠AOB as right angle.


Now, in ΔAOB,


h = 10 cm


p = 6 cm


b = AO


By applying Pythagoras Theorem we have,


h2 = p2 + b2


102 = 62 + AO2


⇒ 100 = 36 + AO2


⇒ AO2 = 100 – 36


⇒ AO2 = 64


⇒ AO = √64 = 8 cm


Also,


OD = AO = 1/2AD [∵ Diagonals of rhombus bisect each other]


⇒ AD = 2 × AO


⇒ AD = 2 × 8


⇒ AD = 16 cm


Thus the length of the other diagonal is 16 cm.


More from this chapter

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1

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9cm., 11cm. and 6cm.

 2

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 4

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 5

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