Question

Parallelogram ABCD is a rectangle.

AC = 4y
BX = y + 4

What is the value of y?
Enter your answer in the box.

y = ___


I'm not sure if I worked it out correctly, so could you explain that as well? Thanks.

Answer 1

`\boxed{\boxed{y=4}}`

Solution-

Properties of the diagonals of a rectangle,

1. The two diagonals are congruent (same length).
2. Each diagonal bisects the other.
3. Each diagonal bisects the other.

So using the first property, length of diagonal AC and BD will be same

`AC=BD`

And using second property,

`BD=2\cdot BX`

Hence,

`AC=2\cdot BX`

Given that,

AC = 4y and BX = y + 4

Putting the values,

`\Rightarrow 4y=2\cdot (y + 4)`

`\Rightarrow 4y=2y + 8`

`\Rightarrow 4y-2y=8`

`\Rightarrow 2y=8`

`\Rightarrow y=4`

Therefore, y=4

Answer 2

A property of rectangle is that the diagonals are equal and bisect eah other.

Given that AC = 4y and BX = y + 4

AC = 2(BX)

⇒ 4y = 2(y + 4) = 2y + 8
⇒ 4y - 2y = 8
⇒ 2y = 8
⇒ y = 4