Question

The approximate length of side XY is units. The approximate length of side YZ is units. The approximate length of side ZX is units. The approximate perimeter of triangle XYZ is units.

Answer 1

ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ = 14√5 units

Explanation:

1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle, the length of this altitude would be: 3 units

2. The length of ZX can be determined through Pythagorean Theorem. If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW. ZW clearly = 3, thus ZX^2 = 3^2 + 3^2 = 18, and ZX = √18 units = 3√2.

3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW. Knowing XW to have a length of 3 units, and YW to have length of 1 unit ⇒ XY^2 = XW^2 + YW^2 = 3^2 + 1^2, and XY = √10.

4. YZ is visualized to have a length of 4 units.

5. Knowing that ZX = 3√2, XY =√10, and YZ = 4 ⇒ Perimeter of ΔXYZ = ZX + XY + YZ = 3√2 + √10 + 4 = 14√5 units. To simplify this, it would be that the Perimeter of ΔXYZ = 14√5 units

Answer 2

The approximate length of side ZX is 4.24 units and the approximate perimeter of triangle XYZ is 11.4 units.

Triangle XYZ

Approximate length of side XY: 3.16 units

Approximate length of side YZ: 4 units

Approximate length of side ZX: 4.24 units

Approximate perimeter of triangle XYZ: 11.4 units

Analysis

We can use the Pythagorean Theorem to calculate the approximate length of side ZX:

ZX = √(XY^2 + YZ^2)

Substituting in the approximate lengths of XY and YZ, we get:

ZX = √(3.16^2 + 4^2)

ZX = √(10.0576 + 16)

ZX = √26.0576

ZX ≈ 4.24 units

To calculate the approximate perimeter of triangle XYZ, we simply add up the approximate lengths of the three sides:

Perimeter = XY + YZ + ZX

Perimeter = 3.16 + 4 + 4.24

Perimeter ≈ 11.4 units

Therefore, the approximate length of side ZX is 4.24 units and the approximate perimeter of triangle XYZ is 11.4 units.