Question

. Find the length of the unknown sides in the following right

angled triangle​

Answer 1

★ How to do :-

Here, we are given with the diagram consisting of a right-angled triangle. We are given with one of the arm's measurement and we are also provided with the measurement of the hypotenuse side. We are not given with the measurement of the base of that triangle. It is represented by a variable 'x'. We are asked to find the value of that variable 'x'. This type of problems can be solved by the property of Pythagoras theorem. This property can only be used to find the measurements of the right angled triangle. So, let's solve!!

$\:$

➤ Solution :-

${\tt \leadsto \underline{\boxed{\tt {ab}^{2} + {bc}^{2} = {ca}^{2}}}}$

${\tt \leadsto {6}^{2} + {x}^{2} = {10}^{2}}$

${\tt \leadsto {x}^{2} = {10}^{2} - {6}^{2}}$

${\tt \leadsto {x}^{2} = 100 - 36}$

${\tt \leadsto {x}^{2} = 64}$

${\tt \leadsto x = \sqrt{64}}$

${\tt \leadsto \orange{\boxed{\tt x = 8 \: \: cm}}}$

$\Huge\therefore$ The value of 'x' in this triangle is 8 cm.

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More to know :-

• The Pythagoras property is the rule which was invented by a scientist named as Pythagoras. He proved this rule and his name was given to this property.
• This rule says that the hypotenuse of the right angled triangle always measures as the sum of square of the measurements of other two sides.