Question

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

Explanation:

Step1: Use the property of rectangle diagonals

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

Step2: Substitute the given expressions

Given \(CO=-3x\) and \(BD = x + 21\). Substituting into \(BD = 2CO\), we 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:

\(x = - 3\)