Question

Aleks help!! i got an answer wrong, but i dont know which one

Answer 1

To find the lengths TX, TW, TU, and UX, we can use the properties of medians in a triangle.

1. Since TX is a median, it divides side AU into two equal parts. So, TU = 2 * TX. Given that UY = 33, we can find TU by dividing UY by 2. Thus, TU = 33 / 2 = 16.5.

2. Similarly, since TW is a median, it divides side AV into two equal parts. So, VW = 2 * TW. Given that VZ = 14, we can find VW by dividing VZ by 2. Thus, VW = 14 / 2 = 7.

3. The centroid of a triangle divides the medians into segments with a ratio of 2:1. This means that ZU is two-thirds of UY and ZT is two-thirds of TZ. Using this information, we can find ZU and ZT.

ZU = (2/3) * UY = (2/3) * 33 = 22.

ZT = (2/3) * TZ = (2/3) * 8 = 5.333 (approximately).

4. To find the length of TX, we can subtract ZT from TZ since TZ = TX + ZT.

TX = TZ - ZT = 8 - 5.333 = 2.667 (approximately).

So, the lengths are:

TX = 2.667 (approximately),

TW = 7,

TU = 16.5,

UX = TU - TX = 16.5 - 2.667 = 13.833 (approximately).

Answer 2

Applying the centroid theorem, the measures are: ZW = 7; ZY = 11; TX = 12.

What is the centroid theorem?

In a triangle, the centroid is located two-thirds of the way from a vertex to the midpoint of the opposite side, according to the centroid theorem, which means that if Z is the centroid of triangle TUV, therefore:

TZ = 2/3(TX)

VZ = 2/3(VW)

UZ = 2/3(UY)

Given:

UY = 33

TZ = 8

VZ = 14

Find ZW:

VZ = 2/3(VW)

14 = 2/3(VW)

42 = 2(VW)

42/2 = VW

VW = 21

ZW = VW - VZ

ZW = 21 - 14

ZW = 7

Find ZY:

ZY = 1/3(UY)

ZY = 1/3(33)

ZY = 11

Find TX:

TZ = 2/3(TX)

8 = 2/3(TX)

24 = 2(TX)

24/2 = TX

12 = TX

TX = 12