Question

ABC is a triangle right angled at C if AC = 4 cm BC = 3 cm find side AB.
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Answer 1

Given

ABC is a triangle where

AC=4 cm

BC=3 cm

According to Pythagoras theorem ,

a²+b²=c²

So, c²-a²=b² (AC is hypotenuse)

So, length of side AB =

$\sqrt{4 { }^{2} } - {3}^{2}$

$= \sqrt{16 - 9}$

$= \sqrt{7}$

$= 2.64$

(approx)

So , AB=2.64cm(approx)

Answer 2

Given:

ABC is a triangle right angled at C and AC = 4 cm BC = 3 cm.

To find: Side AB.

Solution:

Know that ABC is a triangle right angled at C

Apply Pythagoras theorem,

$\[\begin{array}{l} \Rightarrow A{B^2} = A{C^2} + B{C^2}\\ \Rightarrow AB = \sqrt {A{C^2} + B{C^2}} \\ \Rightarrow AB = \sqrt {{4^2} + {3^2}} \\ \Rightarrow AB = \sqrt {16 + 9} \end{array}\]$

Solve further,

$\[\begin{array}{l} \Rightarrow AB = \sqrt {25} \\ \Rightarrow AB = 5\;cm\end{array}\]$

Hence, the length of AB is 5 cm.