WXYZ is a rhombus. Find x.

Question

Answer 1

Keep it simple. Since there's no diagram, go by convention. Draw the 4-sided figure with all sides equal and label it clock-wise alphabetically. Connect the opposite points and label where the two lines intersect E. Realize that a rhombus can be a square or in this case a squished kite. Since point X is opposite point Z and the distance between them is cut in half by point E, you can set ZE's 5x-10 equal to EX's 2x-1 and solve for x. Good luck!

Answer 2

x = 3

E cuts the diagonals in half. each half of one diagonal = the other half of the same diagonal

ZE= EX

5x + 10 = 2x -1

3x = 9

x = 9/3 = 3

x=3

UNLESS

ZE = EY

then

5x+10 = 3x-5

2x = 5

x = -5-10

x = -15,

BUT we can ignore a negative length

so go with x=3

the only positive solution

ZX = 10

WY = 8

the two diagonals are 8 and 10

it's ambiguous whether the problem means an angle of 1 degree or 1 radian

if 1 radian, then sinZ/5 = sin57.3/4 and sinZ =1.05 which is impossible

so 1 must mean 1 degree

then

using law of cosines

e^2 = z^+ w^2 - 2zwCosE

e^2 = 5^2 +4^2 -2(5)(4)Cos1

e = about 8.998 = a side of the rhombus

each side is about 8.998

a rhombus is an "equilateral quadrilateral," with 4 sides all equal, opposite sides parallel and opposite angles equal. angles are 1, 1, 179 and 179 degrees. They sum to 360

It's nearly flat parallelogram, that almost collapsed into a straight line, with nearly zero area.