Question

I need help with these questions ASAP!!!!!

Answer 1

1.)
`x=8√(2)`

2.)
`x=14`

3.)
`x=18√(2)`

4.)
`x=9√(2)`

5.)
`x=4√(2)`

6.)
`x=5√(2)`

7.)
`x=12√(2)`

Explanation:

Use the 45°-45°-90° formula:

`hypotenuse=√(2)*leg`

1.) Insert values:

`x=√(2)*8`

Simplify:

`x=8√(2)`

2.) In a 45°-45°-90° angle, the legs have the same value.

`x=14`

3.) x is the hypotenuse. Insert values:

`x=√(2)*18`

Simplify:

`x=18√(2)`

4.) Insert values:

`18=√(2)*x`

Divide
`√(2)` from both sides:

`(18)/(√(2))=(√(2)*x)/(√(2)) \\\\(18)/(√(2))=x`

Rationalize the left side:

`(√(2))/(√(2))*(18)/(√(2))=x\\\\(18√(2))/(√(4))\\\\(18√(2))/(2) \\\\9√(2)=x`

Simplify:

`x=9√(2)`

5.) Insert values:

`8=√(2)*x`

Divide
`√(2)` from both sides and rationalize:

`(8)/(√(2))=(√(2)*x )/(√(2))\\\\(8)/(√(2))=x`

`(√(2) )/(√(2) ) *(8)/(√(2))\\\\(8√(2))/(√(4)) \\\\(8√(2))/(2)\\\\4√(2)=x`

Simplify:

`x=4√(2)`

6.) 10 is the hypotenuse. Insert values:

`10=√(2)*x`

Divide
`√(2)` from both sides and rationalize:

`(10)/(√(2))=(√(2)*x)/(√(2)) \\\\(10)/(√(2)) =x`

`(√(2))/(√(2))*(10)/(√(2))\\\\(10√(2))/(√(4))\\\\(10√(2))/(2)\\\\5√(2)=x`

Simplify:

`x=5√(2)`

7.) Draw the figure like the squares in problems 3 and 10. The problem says that the perimeter is 48, so divide 48 by 4, which is 12. A side is 12 meters (or a leg). The diagonal is the hypotenuse of a triangle. Insert values:

`x=√(2)*12`

Simplify:

`x=12√(2)`

Finito.