# Ex.6.4 Q7 Squares and Square Roots - NCERT Maths Class 8

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## Question

In a right triangle $$\rm{}ABC$$, $$\rm{}∠B = 90°$$.

(i) If $$AB = 6 \,\rm{ cm}$$, $$BC = 8\, \rm{cm}$$, find $$AC$$

(ii) If $$AC = 13\,\rm{cm},$$  $$BC = 5 \,\rm{cm}$$, find $$AB$$

Video Solution
Squares And Square Roots
Ex 6.4 | Question 7

## Text Solution

What is known?

Two sides right triangle

What is unknown?

One side of the given triangle

Reasoning:

In a right-angle triangle if two sides are given then third side can be calculated using the Pythagoras theorem.

Steps:

(i)

$$AB = 6\;\rm{cm}$$ $$BC = 8\;\rm{cm}$$  $$AC=$$ ?

According to Pythagoras theorem

\begin{align}{\rm{A}}{{\rm{C}}^{\rm{2}}}\,{\rm{ }}&= \;{\rm{A}}{{\rm{B}}^{\rm{2}}}\;{\rm{ + }}\;{\rm{B}}{{\rm{C}}^{\rm{2}}}\\{\rm{A}}{{\rm{C}}^{\rm{2}}}\;{\rm{ }}&= \;{{\rm{(6)}}^{\rm{2}}}\;{\rm{ + }}\;{{\rm{(8)}}^{\rm{2}}}\\{\rm{A}}{{\rm{C}}^{\rm{2}}}\;{\rm{ }}&= \;{\rm{100}}\\\;\,{\rm{AC}}\;{\rm{ }}&= \;\sqrt {{\rm{100}}} \\\;\,{\rm{AC}}\;{\rm{ }}&= \;{\rm{10}}\;{\rm{cm}}\end{align}

(ii)

$$AC = 13\;\rm{cm}$$ , $$BC = 5\;\rm{cm}$$ , $$AB$$=?

According to Pythagoras theorem

\begin{align}{\rm{A}}{{\rm{C}}^{\rm{2}}}\;{\rm{ }}&= \;{\rm{A}}{{\rm{B}}^{\rm{2}}}\;{\rm{ + }}\;{\rm{B}}{{\rm{C}}^{\rm{2}}}\\{{\rm{(13)}}^{\rm{2}}}\;{\rm{ }}&= \;{\rm{A}}{{\rm{B}}^{\rm{2}}}\;{\rm{ + }}\;{{\rm{(5)}}^{\rm{2}}}\\{\rm{169}}\;{\rm{ }}&= \;{\rm{A}}{{\rm{B}}^{\rm{2}}}\;{\rm{ + }}\;{\rm{25}}\\ {\rm{A}}{{\rm{B}}^{\rm{2}}}\;{\rm{ }}&= \;{\rm{169}} - {\rm{25}}\;{\rm{ }}=\;{\rm{144}}\\{\rm{AB}}\;{\rm{ }}&= \;\sqrt {{\rm{144}}} \;{\rm{ }}= \;{\rm{12}}\;{\rm{cm}}\end{align}

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