Question

if the diagonals of a rhomus are. 12 cm and 16 cm , find the lengths of each side

Answer 1

Hello..
Answer...

ABCD is a rhombus

Given :- diagonals are 12cm and 16cm

diagonal 1 (d1) = AC = 16 cm
diagonal 2 (d2) = OB = 12 cm

(one of the property of rhombus = the diagonals bisect each other at 90 degree)

So,
AO = OC = 8cm each
OB = OD = 6cm each

AOB triangle, AOB triangle, DOC triangle and BOC triangle all are right angled triangles.

$AOB \: \: triangle \\ {(AO )}^{2} + {( BO )}^{2} = {(AB)}^{2} \\ {(8)}^{2} + {(6)}^{2} = {(AB)}^{2} \\ 64 + 36 = {(AB)}^{2} \\ 100 = {(AB)}^{2} \\ \sqrt{100} = AB \\ 10 = AB$

(another property of the rhombus = all sides are equal)

So,
AB = 10cm
AD = 10cm
DC = 10cm
BC = 10cm



Hope it helped....
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