If two circles of radii 35 cm and 25 cm touch each other externally, then the length (in cm) of a common tangent is (Rounded off to 2 decimal places)

The correct answer is 59.16.

When two circles touch each other externally, the length of their direct common tangent can be calculated using a standard geometric formula.

Let the radii of the two circles be $r_1$ and $r_2$.
Here, the radius of the first circle, $r_1=35\text{cm}$.
The radius of the second circle, $r_2=25\text{cm}$.

The formula for the length of a direct common tangent ($d$) to two circles with distance between their centers ($D$) is given by:
$d=\sqrt{D^2-{\left(r_1-r_2\right)}^2}$

Since the two circles touch each other externally, the distance between their centers ($D$) is exactly equal to the sum of their radii:
$D=r_1+r_2$
$D=35+25=60\text{cm}$

Substituting the values of $D$, $r_1$, and $r_2$ into the tangent length formula, we get:
$d=\sqrt{{60}^2-{\left(35-25\right)}^2}$
$d=\sqrt{3600-{10}^2}$
$d=\sqrt{3600-100}$
$d=\sqrt{3500}$

Simplifying the square root:
$d=\sqrt{100\times 35}=10\sqrt{35}$

Since $\sqrt{35}\approx 5.9160798$:
$d\approx 10\times 5.91608\approx 59.16\text{cm}$

Therefore, the length of the common tangent rounded off to two decimal places is 59.16 cm.