Answer:
D. 28
Step-by-step explanation:
Please find the attachment.
We have been given that the diagonals of rectangle NOPQ intersect at point R. We are asked to find the value of x.
We will use diagonal property of rectangle, which states that diagonals of rectangle are equal and bisect each other.
Using diagonal property of rectangle, we can conclude that the segment NP is 2 times segment OR, so we can set an equation as:
\(2\times OR=NP\)
Upon substituting the given expressions for both segments we will get,
\(2(3x-4)=5x+20\)
Using distributive property we will get,
\(6x-8=5x+20\)
Subtracting 5x from both sides we will get,
\(6x-5x-8=5x-5x+20\)
\(x-8=20\)
Now, we will add 8 on both sides
\(x-8+8=20+8\)
\(x=28\)
Therefore, the value of x is 28 and option D is the correct choice.
