Question

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 1

Welcome to QC!

Do you think she is correct or no?

Answer 2

yes

Answer 3

And why do u think that?

Answer 4

if you look at the picture the rectangle is half of the square which would make it 2 times bigger

Answer 5

What was the length of SQ

Answer 6

17.89 I think

Answer 7

The length of SQ 16^2 + 8^2 = SQ^2

Answer 8

right

Answer 9

yep

Answer 10

So how did u get that, like show the steps bc it says u have to show work

Answer 11

@Aliannaaaaaaaa ^

Answer 12

Ok I know how to do it Thanks!

Answer 13

Your welcome!, but do you still think shes correct?

Answer 14

idk yet Id have to do the math with both answers and see

Answer 15

ok lmk if u need more help

Answer 16

Rectangle A PQRS


First, we must get the information from the problem of what the length and width was labeled.

Length SR is labeled 14 inches

Width QR is labeled as 7 inches

Now I've got some explaining to do so,

When a diagonal line goes through a rectangle, it splits the rectangle into 2 triangles.

So now, you may have heard of The Pythagorean Theorem. We will be using it to solve the problem. So,

According to The Pythagorean Theorem:

\[c^2 = a^2 + b^2\]
\[ c = length\ of\ the\ diagonal\] \[a = Length\ of\ the\ rectangle\ = 14 inches\] \[b = Width\ of\ the\ rectangle = 7 inches\]
Using what is above, we will come to

\[c^2 = 14^2 + 7^2\]
\[c = √(14^2 + 7^2)\]
So, I believe \[c = 15.65\ inches\]
\[PQRS = SQ = 15.65\ inches\ (Length\ of\ the\ diagonal\ of\ Rectangle) \]

Square B LMNO

LM Square was labeled 7 inches. As we know, all of a square's sides are equal so, all the sides are the same (along with the width which is what we are looking for.

As I stated before "When a diagonal line goes through a rectangle, it splits the rectangle into 2 triangles."

Again, we have to use The Pythagorean Theorem:

\[c^2 = a^2 + b^2\]

\[ c = length\ of\ the\ diagonal\] \[a = Length\ of\ the\ rectangle\ = 14 inches\] \[b = Width\ of\ the\ rectangle = 7 inches\]
\[c^2 = 7^2 + 7^2\]\[c = √(7² + 7²)\] So, I believe \[c = 9.9 inches\]

\[LMNO = OM = 9.9 inches\ (Length\ of\ the\ diagonal\ of\ Square)\]

So, basically what Anna is saying is the length of diagonal SQ is 2x the length of diagonal OM

Answer 17

Anna's calculations are absolutely incorrect.
\[SQ ≠ 2OM\]
\[15.65\ inches ≠ 19.8\ inches\]

Answer 18

She already got the answer 3 days ago but good explanation 😄

Answer 19

ik i did it 4 fun