Question

A contractor is building a pool labeled ABCD on the plans. If AC = 5y + 6 and BD = 8y − 3, what value of y ensures the pool is a rectangle?

−9
9
−3
3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To ensure the pool is a rectangle, the diagonals AC and BD must be equal in length.

Given that AC = 5y + 6 and BD = 8y − 3, we can set them equal to each other:

5y + 6 = 8y - 3

Subtracting 5y from both sides gives:

6 = 3y - 3

Add 3 to both sides:

9 = 3y

Divide both sides by 3:

y = 3

Therefore, the value of y that ensures the pool is a rectangle is 3.