Explanation

• Black part = 1​/8 of the total length

• White part = 1​ /4of the total length

• Grey part = 5.25 cm

• Total length =?

Let total length be $x$ cm.

Then:

$$text{Black} = frac{1}{8}x, quad text{White} = frac{1}{4}x, quad text{Grey} = 5.25 , text{cm}$$

Add them all:

1/8​x+1​/4x+5.25=x

Convert $frac{1}{4}x$ to same denominator:

$$frac{1}{8}x + frac{2}{8}x + 5.25 = x Rightarrow frac{3}{8}x + 5.25 = x$$

Now solve:

x−3/8​x=5.25⇒5/8​x=5.25

Multiply both sides by 8:

5x=42⇒x=42​/5=8.4cm