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In a right angled $Δ A B C$ , if $∠ B = 90 °, A B = 12 cm$ and $B C = 5 cm$ , then what is the value of AC?

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11 cm

12 cm

13 cm

14 cm

answer is C.

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Detailed Solution

It is given that in a right angled

Δ A B C

∠ B = 90 °, A B = 12 cm

and

B C = 5 cm

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''
Write down the given data,
In the triangle ABC, AB = 12 cm and BC = 5 cm.
By Pythagoras theorem,

(Hypotenuse)^{2} = (Opposite side)^{2} + (Adjacent side)^{2}

Apply the above theorem.

⇒ A C 2 = A B 2 + B C 2 ⇒ A C 2 = 122 + 52 ⇒ A C 2 = 144 + 25 ⇒ A C 2 = 169 ⇒ A C = 13

Hence, in the triangle ABC, if AB = 12cm and BC = 5cm, then the value of AC is 13cm.
Therefore, option 3 is correct.

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