Question

Parallelogram ABCD is a rectangle.

AC=5y−2

BD=4y+1



What is the value of y?

Enter your answer in the box.

y =

A rectangle A B C D. Side A B and side C D are parallel. Side A D and B C are parallel. Diagonal B D and A C intersect each other at a point labeled as X.

Answer 1

Because diagonals of a parallelogram are equal, set both problems equal to one another. Solving, you should get y=3

Answer 2

`y=3`

Explanation:

Given: Parallelogram ABCD is a rectangle.

`AC=5y-2` and
`BD=4y+1`

To find: Value of y

Solution: It is given that ABCD is a rectangle, and we know that the opposite sides of a rectangle, and the diagonals of a rectangle are always equal.

As, AC and BD are the diagonals of the rectangle, both will be equal.

So, on equating AC and BD we have,

`AC=BD`

`5y-2=4y+1`

`5y-4y=1+2`

`y=3`

Hence, the value of y is 3.