Question

ength of diagonal ac and bd of rhombus are 6 cm and 8cm respectively.find the length of each side of the rhombus

Answer 1

$\green{\underline{Hey\:mate\: !}}$

$\pink{\underline{\therefore \:Diagonal \:of \:Rhombus \:bisect \:at \:90\degree\:at \:point \:O}}$

AC = 6 cm

DB = 8 cm

$DO = \frac{1}{2}\times 8\\\implies \frac{1}{\cancel 2}\times {\cancel {8}}\\\implies 4 \: cm$

$OC = \frac{1}{2}\times 6\\\implies \frac{1}{\cancel 2}\times {\cancel {6}}\\\implies 3 \: cm$

$\red{\text{Now we know diagonal's of Rhombus bisect at 90\degree.}}$

$\green{\bold{\underline{Use \:pythogorous}}}$

$DC^{2} = OD^{2} + OC^{2} \\ \implies DC= \sqrt{4^{2}\: + \: 3^{2}}\\\implies DC = \sqrt{16+9}\\\implies DC = \sqrt{25} \\\implies DC = 5\: cm$

$\pink{\sf{Sides \:of \:Rhombus\: are\: equal\: that\:means \:all}}$
$\pink{\sf{sides \:are\: measures \:5 \:cm.}}$