Question

1. defg is a rectangle. diagonal df = 5x - 5 and eg = x + 11. find the value of x and the length of each 18) find the values

Explanation:

Step1: Recall property of rectangle diagonals

In a rectangle, the diagonals are equal. So, if \(DF\) and \(EG\) are diagonals of rectangle \(DEFG\), then \(DF = EG\).

Step2: Set up the equation

We are given \(DF=5x - 5\) and \(EG=x + 11\). Setting them equal gives \(5x-5=x + 11\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(5x-x-5=x - x+ 11\), which simplifies to \(4x-5 = 11\). Then add 5 to both sides: \(4x-5 + 5=11 + 5\), so \(4x=16\). Divide both sides by 4: \(\frac{4x}{4}=\frac{16}{4}\), and \(x = 4\).

Step4: Find the length of each diagonal

Substitute \(x = 4\) into the expression for \(DF\) (we could also use the expression for \(EG\)). \(DF=5x-5=5\times4-5=20 - 5=15\). \(EG=x + 11=4+11 = 15\).

Answer:

\(x = 4\), length of each diagonal \(=15\)