Question

Look at the rectangle and the square
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

Answer:

NO. Ada is not correct.

Step-by-step explanation:

Using Pythagorean Theorem, find the length of the diagonal of the rectangle and the square, respectively.

✔️Diagonal of the Rectangle:

$a^2 + b^2 = c^2$

Where,

a = 8 in.

b = 16 in.

c = hypotenuse (longest side of a right ∆)

Plug in the values into the equation

$8^2 + 16^2 = c^2$

$64 + 256 = c^2$

$320 = c^2$

Take the square root of both sides

$\sqrt{320} = \sqrt{c^2}$

$17.9 = c^2$ (nearest tenth)

Length of diagonal SQ = 17.9 in

✔️Diagonal of the Rectangle:

$a^2 + b^2 = c^2$

Where,

a = 8 in.

b = 8 in.

c = hypotenuse (longest side of a right ∆)

Plug in the values into the equation

$8^2 + 8^2 = c^2$

$64 + 64 = c^2$

$128 = c^2$

Take the square root of both sides

$\sqrt{128} = \sqrt{c^2}$

$11.3 = c^2$ (nearest tenth)

Length of diagonal OM = 11.3 in.

SQ is not two times the length of OM.

Therefore, Ada is not correct.

Answer 2

Answer:

No Ada is not correct

Step-by-Step Explanation:

The length of diagonal SQ is not two times the length of diagonal OM. When you split the rectangle using the diagonal you can make a right triangle and use the Pythagorean Theorem to the rest of it. 

This would be the Rectangle:

a^2+b^2=c^2

8^2+16^2=c^2

64+256+c^2

320=c^2

√320

17.8

This would be the Square: 

a^2+b^2=c^2

8^2+8^2=c^2

64+64=c^2

128=c^2

√128

11.3

Now when I divide these answers that I came up with I get 1.7 which is not equal to 2 therefore SQ is not two times bigger than OM. 

I hope this helped :3