Answer:
y=2.4
Explanation:
We know that a rhombus has 4 equal sides, and 2 diagonals which bisect eachother at an angle of 90 degrees.
Simply saying, a rhombus is made up of 4 right angled triangles.
If QR is 3y-2, that means that each other side must be 3y-2 aswell, which means that SQ is also 3y-2
Now we can use the pythagorean theorem to solve for y, given that the base is 2 (length of QU), the height is 2y (length of SU), and the hypotenuse is 3y-2 (length of SQ)
(3y-2)²=2²+2y² (Expand using binomial formula)
9y²-12y+4=4+4y² (Collect similar terms)
5y²-12y=0 (Factor the expression)
y(5y-12)=0
We know that if a product of 2 factors is 0, atleast one must also be 0
So we have to make both factors equal 0
y=0
5y-12=0
5y=12
y=12/5, or 2.4
We see that 2.4 is the only possible solution.
Hope this helps!