NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.3

Question 15

Step 1: Imagine the situation as a right-angled triangle.

• The ladder is the slant side (hypotenuse) = 10 m.
• The distance of the foot of the ladder from the wall is the base = 6 m.
• The height reached on the wall is the perpendicular side. This is what we need to find.

Step 2: Use the Pythagoras Theorem:

\[( ext{Hypotenuse})^2 = ( ext{Base})^2 + ( ext{Height})^2\]

Step 3: Substitute the values:

\[10^2 = 6^2 + ( ext{Height})^2\]

\[100 = 36 + ( ext{Height})^2\]

Step 4: Simplify:

\[( ext{Height})^2 = 100 - 36 = 64\]

Step 5: Take square root:

\[ ext{Height} = \sqrt{64} = 8\, ext{m}\]

Final Answer: The ladder reaches a height of 8 metres on the wall.