Question

the figure below is a square. find the value of x.

Explanation:

Step1: Recall property of square

In a square, the diagonals are equal. So, we set up the equation $7x + 6=4x + 18$.

Step2: Isolate x - terms

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

Step3: Isolate the constant

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:

$4$