Question

Mark (✓) against the correct answer
In ∆ABC, ∠B = 90°, AB = 5 cm and AC = 13 cm. Then, BC = ?



(a) 8 cm
(b) 18 cm
(c) 12 cm
(d) none of these

Answer 1

$$\begin{gathered} \left(c\right)12\mathrm{cm} \\ \begin{array}{l}\text{In a right angle triangle:}\\ {\text{AC}}^2={\text{AB}}^2+{\text{BC}}^2\text{(Pythagoras theorem)}\\ =>{\text{BC}}^2={13}^2-5^2\\ {\text{=> BC}}^2=169-25\\ =>{\text{BC}}^2=144\\ =>\text{BC =±12}\end{array} \\ \text{The length cannot be negative.} \\ \text{∴ BC= 12 cm} \end{gathered}$$