Question

Hello guys can someone help me with this, my dead line is too close hehe

Answer 1

*Note:- The values in the red boxes are final answers for that question!!

Answer 2

16 x = 2

17.
`\bold{\overline{MA} = 12\;meters}\\`

18.
`\bold{\overline {MZ} = 16.97\;meters}`

19.
`\bold{\overline {AE} = 16.97\;meters}`

20. Perimeter = 48 meters

*** Please look at my comment on question 20 at the very bottom of the explanation

Explanation:

Since the given figure is a square, all four sides must be equal

Therefore

`\overline {MZ} = \overline {EZ}`

Plugging in given expressions for
`\overline {MZ} \;\text{and}\; \overline {EZ}` we get:
5x + 2 = 9x -6

Subtract 5x from both sides:
5x - 5x + 2 = 9x - 5x -6
2 = 4x - 6

Add 6 both sides:
2 + 6 = 4x - 6 + 6
8 = 4x

Switch sides:
4x = 8

Divide both sides by 4:
4x/4 = 8/4
x = 2 (Answer #16)

Therefore

Keeping in mind that all four sides are equal,

`\bold{\overline{MA} = 12}\\` (Answer # 17)

`\text{Therefore $ \overline {EZ} $ \ is also 12}`

(Can verify this with plugging in x =2 into 9x - 6 giving
9(2) - 6 = 18 - 6 =12

and also ME =12)

To find
`\overline {MZ}` since MZ is the diagonal and the angles of a square are all 90°,

in ΔMZE, MZ is the hypotenuse of a right triangle with legs ME and EZ
Therefore
MZ² = ME² + EZ²
= 12² + 12²

= 2 (12²)

Therefore

`\overline{MZ} = √(2 * 12^2)\\\\= 12√(2)\\`since √a² = a

`\= 16.97 \;meters` (Answer #18)

In a square the diagonals are equal so

`\bold{\overline{AE} = \overline{MZ} = 16.97\;meters}` (Answer #19)

Perimeter of the square = 4 x length of each side
= 4 x 12

= 48 meters (Answer #20)

*** In question 20 which is rather confusing, I have taken only the outer edges of the square

If they mean the length of all lines including the diagonals which make up the maze, you will have to add the two diagonals which means 48 + 16.97 + 16.97 = 81.94 meters

Perimeter refers to the outer edges so I believe the answer of 48 is correct. Just not 100% sure on this. Sorry