Uv = 8 and wx=5 find the missing measure of a rhombus

The missing measures of the rhombus are: , , , and

The given parameters are:

All sides of a rhombus are equal.

So, we have:

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

This gives

Subtract 25 from both sides

Rewrite as:

Take square roots

This means that:

Hence, the missing side lengths are: , , , and

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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: