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HELPPP I WILL MARK BRAINIEST!!! Look at the rectangle and the square: Sam says that the length of diagonal SQ is two times the length of diagonal OM. Is Sam correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.

HELPPP I WILL MARK BRAINIEST Look At The Rectangle And The Square Sam Says That The Length Of Diagonal SQ Is Two Times The Length Of Diagonal OM Is Sam Correct class=

Sagot :

the length of the square is a = 6 in.

the length of the diagonal is,

[tex]d=\sqrt[]{2}a[/tex]

where a= side of the square,

[tex]\begin{gathered} d=\sqrt[]{2}\times6 \\ d=6\sqrt[]{2} \end{gathered}[/tex]

in rectangle, the length of the diagonal SQ,

[tex]\begin{gathered} SQ=\sqrt[]{6^2+12^2} \\ SQ=\sqrt[]{36+144} \\ \end{gathered}[/tex][tex]\begin{gathered} SQ=\sqrt[]{180} \\ SQ=\sqrt[]{36\times5} \\ SQ=6\sqrt[]{5} \end{gathered}[/tex]

so it is clear that 2 x OM

[tex]\begin{gathered} 2\times6\sqrt[]{2} \\ 12\sqrt[]{2} \end{gathered}[/tex]

so it is not equal to SQ.

it means the sam was wrong.

he length of diagonal SQ is not equal to two times the length of diagonal OM.