Question

If the following figure is a rectangle, find the missing measures. round all answers to 1 decimal place if necessary.

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Answer 1

VW=31

WX=19

YW=36.4 or
`√(1322)`

ZX= 18.2 or
`(√(1322) )/(2)`

VX= 36.4 or
`√(1322)`

Explanation:

Since the figure is a rectangle certain rules about the lengths of its sides and diagonals apply. One such rule is that opposite sides are equal, so YX=VW and VY=WX. Then you need to find the length of the diagonals by using the Pythagorean theorem since the diagonals cut the rectangle into two right triangles. By using the theorem you can find that the length of the diagonal YW is 36.4 or
`√(1322)`, and since all diagonals are congruent VX is the same. Finally, in rectangle diagonals bisect each other, therefore part of one must be half of the total, so ZX must be half of VX.