Question

Rhombus ABCD if ab = 10 cm and diagonal AC = 12 cm find the length of a diagonal BD​

Answer 1

Answer: BD=16cm

Step-by-step explanation:

Use pythogorus theorm it will help u ...

Answer 2

$ABCD \:is \: Rhombus .$

$Diagonal \: AC = 12 \:cm , \:and \: AB = 10\:cm$

$\blue {( Diagonals \: bisects\:perpendicularly \:}\\\blue{ in \: a \: Rhombus )}$

$OA = \frac{AC}{2} \\= \frac{12}{2} \\= 6 \:cm$

$and \: AB = 10 \:cm$

$In \: \triangle AOB , \angle {AOB} = 90\degree$

$\pink {( By \: Phythagorean \:theorem )}$

$AB^{2} = OA^{2} + OB^{2}$

$\implies 10^{2} = 6^{2} + OB^{2}$

$\implies 100 - 36 = OB^{2}$

$\implies 64 = OB^{2}$

$\implies 8^{2} = OB^{2}$

$\implies OB = 8 \:cm$

$Now, Diagonal (BD) = 2\times OB \\= 2 \times 8 \\= 16 \:cm$

Therefore.,

$\red{ Length \:of \: the \: diagonal \:BD} \green {= 16\:cm }$

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