NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.4

Question 9

Step 1: First, add the two parts of \(AC\).

We are given: \(AD = 4\,\text{cm}\), \(CD = 5\,\text{cm}\).

So, \(AC = AD + CD = 4 + 5 = 9\,\text{cm}.\)

Step 2: Use the property of a right triangle with altitude drawn to the hypotenuse.

If \(BD\) is perpendicular to \(AC\), then: \(BD^2 = AD \times CD.\)

Substitute values: \(BD^2 = 4 \times 5 = 20.\)

So, \(BD = \sqrt{20} = 2\sqrt{5}\,\text{cm}.\)

Step 3: To find side \(AB\), use another property of the same theorem:

\(AB^2 = AD \times AC.\)

Substitute values: \(AB^2 = 4 \times 9 = 36.\)

So, \(AB = \sqrt{36} = 6\,\text{cm}.\)

Final Answer: \(BD = 2\sqrt{5}\,\text{cm}\) and \(AB = 6\,\text{cm}.\)