Question

In the adjacent figure ABCD is a rhombus whose diagonal intersect at O if a b equal 10 cm and diagonal BD equal 16 cm find the length of diagonal AC

Answer 1

$\underline{SOLUTION}$ ➡

In the above figure,

AB = BC = CD = AD = 10 cm

Diagonal BD = 16 cm

•°• BO = OD = 8 cm [ °•° The diagonal of a rhombus bisect each other at right angles ]

And,

AC is perpendicular on BD

So, AO is perpendicular on OD

•°• In AOD triangle ,

$\angle{AOD}$ = 90°

$AD {}^{2} = (OA) {}^{2} + (OD) {}^{2} \\ \\ = > (10) { }^{2} = (OA) {}^{2} + (8) {}^{2} \\ \\ = > 100 = (OA) {}^{2} + 64 \\ \\ = > (OA) {}^{2} = 100 - 64 \\ \\ = > (OA) {}^{2} = 36 \\ \\ = > OA= \sqrt{36} \\ \\ = > OA= 6 \: \: cm \\ \\ \\ Now, \: \: AC \: = 2 \times OA \\ \\ = > AC =( 2 \times 6) \: cm \\ \\ = > AC = 12 \: cm$

$\underline{ANSWER}$ ➡

$Length \: of \: AC \: = 12 \: cm \: .$

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