Question

ABCD is a rhombus whose diagonals AC and BD intersect at a point o such that AC= 6cm and BD=8cm. find side of rhombus

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

$\Large{\underline{\underline{\bold{✯Given:}}}}$

• ABCD is a Rhombus.
• AC and BD are diagonals of the given rhombus which intersect at O.
• AC = 6cm & BD = 8cm

$\Large{\underline{\underline{\red{\bold{➸To\;Find:}}}}}$

• Length of Side of Rhombus.

$\Large{\underline{\underline{\blue{\bold{✄Solution:}}}}}$

Let's, The side be x

Take a right angle triangle.

In Triangle AOC, Angle AOC = 90°

• AO = OC → AC/2 => 6/2 = 3cm
• BO = OD → BD/2 => 8/2 = 4cm

By Pythagoras Theorem

$\boxed{\green{\sf{(Hypothenuse)² = (Side)²+(Side)²}}}$

$→\;{\sf{ {x}^{2} = {3}^{2} + {4}^{2} }} \\→\;{\sf{ x = \sqrt{(9 + 16)} }}\\ →\;{\sf{x = \sqrt{25} }} \\→\;{\sf{ x = \sqrt{ ({5})^{2} }}} \\→\;{\bf{ x = 5cm}}$

• Length of Side of Rhombus ☞ $\red{\bold{5cm}}$

$\boxed{\tt{@MrSovereign}}$

Hope This Helps!!