Question

In a rectangle ABCD ,the diagonals intersect at o . correct the mistakes in the following. 1)AO=6cm ,BO=4.5cm,AB=7.5cm. please answer this question.​

Answer 1

​$\textbf{Given:}$

$\textsf{In a rectangle ABCD ,the diagonals intersect at O and}$

$\textsf{AO=6cm ,BO=4.5cm,AB=7.5cm}$

$\textbf{To find:}$

$\textsf{The mistakes in the given data}$

$\textbf{Solution:}$

$\textbf{Concept used:}$

$\boxed{\begin{minipage}{7cm} \\\textsf{1.\;Diagonals of rectangle bisect each other}\\\\\textsf{2.\;Diagonals of rectangle are equal in length} \end{minipage}}$

$\implies\mathsf{OA=OC\;\;\&\;\;OB=OD}$

$\implies\mathsf{OA=OC=6\;\;\&\;\;OB=OD=4.5}$

$\mathsf{AC=OA+OC=6+6=12\;cm}$

$\mathsf{BD=OB+OD=4.5+4.5=9}$

$\mathsf{Length\;of\;AC\;{\neq}\;Length\;of\;BD}$

$\textsf{But, length of the diagonals should be equal}$

$\mathsf{So\;it\;should\;be\;OA=OB}$

$\textbf{Find more:}$

Answer 2

Step-by-step explanation:

⟹OA=OC&OB=OD

\implies\mathsf{OA=OC=6\;\;\&\;\;OB=OD=4.5}⟹OA=OC=6&OB=OD=4.5

\mathsf{AC=OA+OC=6+6=12\;cm}AC=OA+OC=6+6=12cm

\mathsf{BD=OB+OD=4.5+4.5=9}BD=OB+OD=4.5+4.5=9

\mathsf{Length\;of\;AC\;{\neq}\;Length\;of\;BD}LengthofAC



=LengthofBD

\textsf{But, length of the diagonals should be equal}But, length of the diagonals should be equal

\mathsf{So\;it\;should\;be\;OA=OB}SoitshouldbeOA=OB