Given, ∆ ABC is right-angled at C. If $A C = 5 c m$ and $B C = 12 c m$ find the length of $A B$ .

[3 marks]

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Solution

Given: $A C = 5 c m, B C = 12 c m$
Let $A B$ be $x c m$ .

In right angled triangle $△ A B C$ , by Pythagoras theorem
$(H y p o t e n u s e)^{2} = (B a s e)^{2} + (P e r p e n d i c u l a r)^{2}$
[1 mark]

$\Rightarrow (A B)^{2} = (A C)^{2} + (B C)^{2} \Rightarrow x^{2} = (5 c m)^{2} + (12 c m)^{2} \Rightarrow x^{2} = 25 c m^{2} + 144 c m^{2} = 169 c m^{2} \Rightarrow x = \sqrt{169 c m^{2}} = 13 c m Thus, the length of A B is 13 c m .$
[2 marks]

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Given, ∆ ABC is right-angled at C. If AC=5 cm and BC=12 cm find the length of AB. [3 marks]

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