Question

i) What should be the shortest length of the connecting

support base so that the fireman reaches the building

where fire broke out.
if height is 120 m and base is 50m far​

Answer 1

$shortest \: distance \: is \: hypotenuse \\ hypotenuse \: = \sqrt{120 {}^{2} + 50 {}^{2} } \\ = \sqrt{14400 \ +2500 } \\ = \sqrt{16900 } \\ = 130 \: m$

Answer 2

Given: Height is 120 m and base is 50m far​.

To find: The shortest length of the connecting support base so that the fireman reaches the building where fire broke out.

Solution: The shortest length of the connecting support base so that the fireman reaches the building where fire broke out is 130 m.

In the given question, the height of the building, the length of the support base and the distance between the base and the building form a right-angled triangle. The perpendicular, base and hypotenuse correspond to these lengths as shown below.

$hypotenuse^{2} = perpendicular^{2} + base^{2}$

$support \: base^{2} = building^{2} + base^{2}$

Now, the lengths are substituted in the formula and the shortest length of the connecting support base is calculated as shown below.

$support \: base^{2} = 120^{2} + 50^{2}$

$support \: base = \sqrt{16900}$

                    $= 130 \: m$

Therefore, the shortest length of the connecting support base so that the fireman reaches the building where fire broke out is 130 m.