Question

To Clean the minaret top a ladder was built. If the height of the is 5m and the ladder needs to be placed at a distance of 12 m from the base , how long should the ladder be?

please answer in full steps​

Answer 1

Please refer attachment for pictorial representation.

★ Given:

Length of the minaret = 5 m

Distance from which the ladder must be kept = 12 m

Height of the ladder = x

★ Solution:

From the attached picture, we can see that the figure formed is a right angled triangle.

We know its:

Base = 12 m

Altitude [Height] = 5 m

Applying the Pythagoras theorem:

Altitude² + Base² = Hypotenuse²

5² + 12² = Hypotenuse²

25 + 144 = Hypotenuse²

169 = Hypotenuse²

Hypotenuse² = 169

So, Hypotenuse = √169

Hypotenuse = 13 m

Hence the height of the ladder must be 13 m.

Knowledge Bytes:

→ The Pythagoras Theorem

The Pythagoras theorem which is a fundamental mathematics theorem states that the sum of the squares of the altitude and the base of any right angled triangle will give us the square of the hypotenuse.

So, the length of the hypotenuse will be the root of the hypotenuse square. From this theorem, two more equations can be formed:

Altitude² = Hypotenuse² - Base²

Base² = Hypotenuse² - Altitude²