Question

The diagonal of a square is x what is the perimeter of the square

Answer 1

Answer:

2$\sqrt{2}$ x

Step-by-step explanation:

The diagonal divides the square into 2 right angles with legs s and hypotenuse x

Using Pythagoras' identity on one of the right triangles, then

s² + s² = x²

2s² = x² ( divide both sides by 2 )

s² = $\frac{x^2}{2}$ ( take the square root of both sides )

s = $\sqrt{\frac{x^2}{2} }$ = $\frac{x}{\sqrt{2} }$

Thus

perimeter = 4s = 4 × $\frac{x}{\sqrt{2} }$ = $\frac{4x}{\sqrt{2} }$

Multiply numerator/ denominator by $\sqrt{2}$

perimeter = $\frac{4x\sqrt{2} }{2}$ = 2$\sqrt{2}$ x