Question

 ABC is right-angled at C. If AC = 5 cm and BC = 12 cm find the length of AB.

Answer 1

Answer:

The length of side AB = $13$ cm.

Step-by-step explanation:

Given : ΔABC is right-angled at C.

          $AC=5$ cm

          $BC=12$ cm

To find : The length of side AB.

Solution :

• It is given that the ΔABC is right-angled at C.

          $AC=5$ cm

          $BC=12$ cm

• We have to find the length of side AB.
• To find the third side of a triangle, we have to apply the Pythagoras theorem to  the given triangle.
• We know that,

       Pythagoras theorem states that, " In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides."

• Applying Pythagoras theorem to the ΔABC, we get

       $(AB)^{2} =(AC)^{2} +(BC)^{2}$

                $=5^{2} +12^{2}$

                $=25+144$

                $= 169$

•  Taking square roots, we get

       ∴ $AB= \sqrt{169}$

               $=13$

• ∴ The length of side AB = $13$ cm.