If you want to put a 4x8 piece of plywood through a 3 foot square opening in your ceiling by turning it diagonally is the opening big enough? use a 45-45-90 since its a square

Yes, the 3 foot 3 foot square opening in your ceiling is big enough to insert a  4x8 piece of plywood.

In  a 3x3 foot square, we can form two right triangles with same diagonal side or hypotenuse. .

Using the Pythagorean theorem/formula, we can find the length of the hypotenuse or the longest side of the triangle ( c) given the two sides a and b

Substitute values a=3 and b=3 to formula

a^2^+b^2^=C^2^=

3^2^+3^2^=C^2^=

9+9= C^2^

C= square root of 18

C=4.24 

A 4x8 piece of plywood can be inserted in a 4.24 opening diagonally.

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!

the answer is 489

step-by-step explanation: