Question

Find the exact value of x.

Answer 1

Answer:

x is 8√2.

Step-by-step explanation:

Answer 2

Answer:

8√2

Step-by-step explanation:

Idea 1 : (Pythagorean theorem)

2x² = 16²

then

2x² = 256

then

x² = 256/2 = 128

then

x = √128

then

x = √(64×2)

then

x = √64 × √2

then

x = 8√2

………………………………………………………

Idea 2 : (diagonal of a square)

16 is the diagonal of a square with side square of lengths x

Then

x√2 = 16

Then

$x = \frac{16}{\sqrt{2} } =\frac{8\times2}{\sqrt{2} } =\frac{8\times\sqrt{2} \times \sqrt{2} }{\sqrt{2} } =8\sqrt{2}$