The diagonal of a square is x units. What is the area of the square in terms of x?
o 3x?square units
Ox?square units
2x square units
o £x square units

(√2)x/2 or (√2/2)x

Step-by-step explanation:

Let's draw two squares, one with diagonal length x and the other with diagonal length √2.  In the second case, the side length is 1, which you can confirm by recalling that 1^2 + 1^2 = 2*1^2 and √2*1^2 = √2.

These two squares are similar, even if they're of different sizes.

Writing an equation of ratios, we get:

  side length               1

=

          x                       √2

Then (side length)*√2 = x (after cross-multiplication)

and so (side length) = x/√2 or (√2)x/2 or (√2/2)x

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign