Respuesta :

Matheng

Answer:

  • TU = UV = VW = WT = 8
  • WX = UX = 5
  • XV = XT = √39

Step-by-step explanation:

At first we should know the following about the rhombus

1) All sides are congruent

2) The diagonals are perpendicular and bisects each other.

Given UV = 8 and WX = 5

So, according to (1)

TU = UV = VW = WT = 8

And according to (2)

WX = UX = 5

And ΔWXV is a right triangle at ∠x

So, XV² = WV² - WX² = 8² - 5² = 64 - 25 = 39

∴XV = √39

So, XV = XT = √39

So, the missing measure of a rhombus are as following:

  • TU = UV = VW = WT = 8
  • WX = UX = 5
  • XV = XT = √39
MrRoyal

The missing measures of the rhombus are: [tex]TU = 8[/tex], [tex]WT=8[/tex], [tex]WV = 8[/tex], [tex]TX = 6.24[/tex] and [tex]XU = 5[/tex]

The given parameters are:

[tex]UV = 8[/tex]

[tex]WX = 5[/tex]

All sides of a rhombus are equal.

So, we have:

[tex]TU = 8[/tex]

[tex]WT=8[/tex]

[tex]WV = 8[/tex]

The diagonals of a rhombus are perpendicular; this means that the triangle WXV is right-angled.

So, we can make use of the following Pythagoras theorem

[tex]WV^2 = WX^2 + XV^2[/tex]

This gives

[tex]8^2 = 5^2 + XV^2[/tex]

[tex]64 = 25 + XV^2[/tex]

Subtract 25 from both sides

[tex]64 - 25 = XV^2[/tex]

[tex]39 = XV^2[/tex]

Rewrite as:

[tex]XV^2 = 39[/tex]

Take square roots

[tex]XV = 6.24[/tex]

This means that:

[tex]XV =TX = 6.24[/tex]

[tex]WX =XU = 5[/tex]

Hence, the missing side lengths are: [tex]TU = 8[/tex], [tex]WT=8[/tex], [tex]WV = 8[/tex], [tex]TX = 6.24[/tex] and [tex]XU = 5[/tex]

Read more about rhombus at:

https://brainly.com/question/2765283

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