Question

help please

Answer 1

Look at the rectangle and the square:

A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 16 inches, and the width QR is labeled as 8 inches. The side LM of the square is labeled as 8 inches.

Ada says that the length of diagonal SQ is two times the length of diagonal OM.

Is Ada correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.

Answer 2

@Michele_Laino PLEASE HELP

Answer 3

@Michele_Laino

Answer 4

here the lenght of the rectangle is:
\[{d_R} = \sqrt {{{16}^2} + {8^2}} = ...?\]

Answer 5

oops..the length of the diagonal of the rectangle

Answer 6

please complete

Answer 7

whereas the length of the diagonal of the square is:
\[{d_S} = \sqrt {{8^2} + {8^2}} = ...?\]

Answer 8

please, try to compute the diagonals \(d_R\) and \(d_S\), what do you get?

Answer 9

in order to compute the lengths of those diagonals, I used the theorem of Pitagora

Answer 10

ok so im not sure though sorry

Answer 11

hint:
after a simplification, we can write this:

\[\begin{gathered}

{d_R} = \sqrt {{{16}^2} + {8^2}} = \sqrt {4 \cdot {8^2} + {8^2}} = 8\sqrt 5 \hfill \\
\hfill \\
{d_S} = \sqrt {{8^2} + {8^2}} = 8\sqrt 2 \hfill \\
\end{gathered} \]

Answer 12

so the ratio \(d_R/d_S\), is:
\[\frac{{{d_R}}}{{{d_S}}} = \frac{{8\sqrt 5 }}{{8\sqrt 2 }} = \sqrt {\frac{5}{2}} \]
what can you conclude?

Answer 13

ok i did it on a paper now can you explain the answe to me

Answer 14

@Michele_Laino

Answer 15

@Michele_Laino

Answer 16

this is my answer am i correct?



Ada is wrong. The length of diagonal SQ is NOT two times the length of diagonal OM.

dr/ds = 8square root 5 over 8square root 2 = 5square root2

Answer 17

correct!