Question

In triangle ABC, LC = 90°, AC = BC = 6cm, find AB​

Answer 1

$\textbf{Concept:}$

$\textsf{Pythagors theorem:}$

$\textsf{In a right angled triangle, square on the hypotenuse is equal}$

$\textsf{to sum of the squares on the other two sides}$

$\textbf{Given:}$

$\angle{C}=90^{\circ}\;\text{and}\;AC=BC=6\;\text{cm}$

$\text{By pythagoras theorem}$

$AB^2=AC^2+BC^2$

$AB^2=6^2+6^2$

$AB^2=36+36$

$AB^2=2{\times}36$

$\bf\;AB=6\sqrt{2}$

$\therefore\textbf{The length of AB is 6\sqrt{2} cm}$

Find more:

∆PQR is an isosceles triangle ,right angled at R . prove that PQ^2=2PR^2

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Answer 2

Given:

∠C = 90°

AC = BC = 6 cm

To Find:

AB = ?

Solution:

On applying Pythagoras theorem, we get

$AB^2=AC^2+BC^2$

On putting the values in the above expression, we get

$AB^2=6^2+6^2$

$AB^2=36+36$

$AB^2=72$

$AB=\sqrt[6]{2} \ cm$

Thus, The value of side AB will be "6√2 cm".