Question

The diagonals of a quadrilateral are of lenghts 6cm and 8cm. If the diagonals bisect each other at right angles, what is the length of each side of the quadrilateral?

Answer 1

Hello user☺☺

Let the ABCD be the quadrilateral.

So, According to the question, we have

AO = OC and OB =OD
Also, Angles made by the intersection of diagonal of it will be 90° each.

Now, in triangle AOB, BOC,COD and AOD, we have

AB^2 = 3^2 + 4^2..... (1) [by Pythagoras theorem]

So, AB = 5 cm

Similarly,

BC = CD = AD = (3^2 + 4^2)^1/2 = 5 cm.

Hope it works☺☺
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You an also refer to the Attachment for the solution.-

Answer 2

$\bf{\underline{\huge{ANSWER}}}$

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$\underline{\bf{\large{GIVEN}}}$

In a quadrilateral ABCD : -

The diagonals measure 6 cm and 8 cm.

The diagonals bisect each other at right angles at O.

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$\underline{\bf{\large{ TO \: FIND }}}$

Lenght of each side of the quadrilateral.

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$\underline{\bf{\large{ SOLUTION}}}$

OA = 3 cm

OB = 4 cm

OC = 3 cm

OD = 4 cm

Using pythageorus theorem :

( OA )^2 + ( OB )^2 = ( AB )^2

( 3 )^2 + ( 4 )^2 = ( AB )^2

9 + 16 = ( AB )^2

25 = ( AB )^2

AB = √25 = 5 cm

Applying the same formula , we find that each side measures 5 cm. Since , the lengths and bases are same , the hypotenuses will also be same.

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$\underline{\bf{\large{ ANS}}}$

The sides of the quadrilateral measure 5 cm each.

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#BE BRAINLY

@Sanskriti141