Question

Solve this using Pythagoras Theorem.
An insect 8m away from the foot of the lamp post which is 6m tall crawls towards it.After moving through a distance its distance from the top of the lamp post is equal to the distance it has moved. How far is the insect away from the foot of the lamp post?

Answer 1

Let us recall some of the properties of a right angled triangle which we have already

learnt.

1. The side opposite to right angle is called hypotenuse.

2. In a right angled triangle, hypotenuse is the longest side.

3. In an isosceles right angled triangle, each acute angle is 45°.

4. Area of a right angled triangle is half the product of the sides

containing the right angle.

5. The perpendicular drawn from the right angled vertex to the

hypotenuse divides the triangle into two similar triangles which are similar to the

given right angled triangle.

Now, let us learn one more very interesting property about right angled triangles.

To understand the property, do the following activity.

Construct a ABC with AB = 4cm, BC = 3cm, AC = 5cm.

Observe that ABC will be exactly 90°.

Construct squares on all the three sides and divide

them into squares of sides 1cm each.

Now, count the number of small squares on all the

three sides. They are 9, 16 and 25. If we add 9 and

16, we get 25. Repeat this activity for right angled

triangles with sides, {6cm, 8cm and 10cm}, {5cm,

12cm, 13cm} etc.

What do we infer from this? We can infer that,

"In a right angled triangle, the square on the hypotenuse is equal to the sum of

the squares on the other two sides".

This statement which gives the relationship between areas of sides of a right angled

triangle is called Pythagoras theorem, named after the Greek mathematician

Pythagoras, who lived around 500BC. This theorem which is used in many branches

of mathematics has attracted the attention of many mathematicians and today we

have hundreds of varieties of proofs for it.

The statement of Pythagoras theorem can be proved practically by another way.

This was given by Henry Perigal (1830). Hence, it is called Perigal

dissection.

Answer 2

Hope this helps you...