Question

 A triangular colourful scenery is made on a wall with sides 25cm, 25cm and 40cm. A golden thread is to hang from the vertex so as to just reach the side 40cm perpendicularly. How much length of the golden thread is required? *​

Answer 1

Solution :-

Given that, sides of triangular colourful scenery are 25cm, 25cm and 40cm.

As we can see two sides are 25cm each . Therefore, we can conclude that, the scenery is in the shape of a Isosceles triangle with two sides as 25cm and base as 40cm.

Now, we know that, Perpendicular on base of a isosceles triangle bisect the base into two equal parts.

So, By pythagoras theorem we get,

→ (Perpendicular)² + (Base/2)² = (Equal side)²

Putting value as Base = 40cm and Equal side as 25cm , we get,

→ (Perpendicular)² + (40/2)² = (25)²

→ (Perpendicular)² + (20)² = (25)²

→ (Perpendicular)² + 400 = 625

→ (Perpendicular)² = 625 - 400

→ (Perpendicular)² = 225

→ (Perpendicular)² = (15)²

Square - root both sides now, we get,

→ Perpendicular = 15 cm. (Ans.)

Hence, length of the golden thread is 15cm.