Question

the figure below is a square. find the value of x.
a
d
b
c
7x + 6
4x + 18
x = ?

Explanation:

Step1: Recall property of square diagonals

In a square, the diagonals bisect each other and are equal. So, \(7x + 6=4x + 18\).

Step2: Isolate x - terms

Subtract \(4x\) from both sides: \(7x-4x + 6=4x-4x + 18\), which simplifies to \(3x+6 = 18\).

Step3: Isolate the constant - term

Subtract 6 from both sides: \(3x+6 - 6=18 - 6\), getting \(3x=12\).

Step4: Solve for x

Divide both sides by 3: \(\frac{3x}{3}=\frac{12}{3}\), so \(x = 4\).

Answer:

\(4\)