Question

given the rectangle abcd as shown, find the value for x if do = 5x - 9 and co = x + 7. (1 point) x = 4

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So, \(DO = CO\).
$$5x - 9=x + 7$$

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides:
$$5x-x-9=x - x+ 7$$
$$4x-9 = 7$$
Add \(9\) to both sides:
$$4x-9 + 9=7 + 9$$
$$4x=16$$
Divide both sides by \(4\):
$$\frac{4x}{4}=\frac{16}{4}$$
$$x = 4$$

Answer:

\(x = 4\)