Question

image long description
the rectangle abcd is given as shown. find x if co = -3x and bd = x + 21

Explanation:

Step1: Recall the property of rectangle's diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(BD = 2CO\).

Step2: Substitute the given expressions

Since \(BD=x + 21\) and \(CO=-3x\), we substitute into \(BD = 2CO\) to get \(x + 21=2(-3x)\).

Step3: Solve the equation

Expand the right - hand side: \(x + 21=-6x\).
Add \(6x\) to both sides: \(x+6x + 21=-6x+6x\), which simplifies to \(7x+21 = 0\).
Subtract 21 from both sides: \(7x+21-21=0 - 21\), so \(7x=-21\).
Divide both sides by 7: \(x=\frac{-21}{7}=-3\).

Answer:

\(x=-3\)