Question

Parallelogram ABCD ​ is a rectangle.

AC=6y−1

BD=4y+13

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

The value of y is: 7

Explanation:

The figure of the rectangle ABCD is attached to the answer.

We are given that Parallelogram ABCD ​ is a rectangle.

AC=6y−1

BD=4y+13

Diagonal BD and AC intersect each other at a point labeled as X.

Also we know that: The two diagonals of a rectangle are equal in length and bisect each other.

i.e. length of AC=BD

Hence 6y-1=4y+13

⇒ 6y-4y=13+1

⇒ 2y=14

⇒ y=7

Hence, AC=6×7-1=42-1=41

BD=4×7+13=41

Hence, the value of y is 7.