Answered

Discover new information and get your questions answered with IDNLearn.com. Get prompt and accurate answers to your questions from our experts who are always ready to help.

1. In a rectangle [tex]\(PQRS\)[/tex], [tex]\(PR\)[/tex] and [tex]\(QS\)[/tex] are diagonals intersecting at [tex]\(O\)[/tex]. If [tex]\(OP = 2y + 3\)[/tex] and [tex]\(OS = 3y + 1\)[/tex], find the value of [tex]\(y\)[/tex].

Sagot :

GinnyAnsweridn
In a rectangle [tex]\( PQRS \)[/tex], the diagonals [tex]\( PR \)[/tex] and [tex]\( QS \)[/tex] intersect at point [tex]\( O \)[/tex]. When two diagonals of a rectangle intersect, they bisect each other. This means that the segments formed by the diagonals are equal. Therefore, we have:

[tex]\[ OP = OS \][/tex]

Given the expressions:
[tex]\[ OP = 2y + 3 \][/tex]
[tex]\[ OS = 3y + 1 \][/tex]

We can set these two expressions equal to each other since [tex]\( OP = OS \)[/tex]:

[tex]\[ 2y + 3 = 3y + 1 \][/tex]

Now, let's solve this equation for [tex]\( y \)[/tex]. First, subtract [tex]\( 2y \)[/tex] from both sides of the equation:

[tex]\[ 3 = y + 1 \][/tex]

Next, subtract 1 from both sides to isolate [tex]\( y \)[/tex]:

[tex]\[ 2 = y \][/tex]

Thus, the value of [tex]\( y \)[/tex] is:

[tex]\[ y = 2 \][/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.