[tex] \large{ \tt{❃ \: STEP - BY - STEP \: EXPLANATION}} : [/tex]
- We're provided : In right angled triangle PQR , The length of of PR & length of PQ are 10 cm & 6 cm respectively & we're asked to find out the length of OR.
- You need to know : The longest side, which is the opposite side of right angle is the hypotenuse ( h ) . When the reference angle is not given , You can assume the remaining sides either perpendicular ( p ) or base ( b ) .
- Here , Hypotenuse ( h ) = 10 cm , Base ( b ) = ? & Perpendicular ( P ) = 6 cm
- Before solving, You will have to know : The square of the hypotenuse of a right - angled triangle is equal to the sum of square of the remaining two sides.
[tex] \large{ \tt{❁ \: LET'S\: START}} : [/tex]
[tex] \boxed {\large{ \bf {\: ♕ \: {h}^{2} = {p}^{2} + {b}^{2} }}}[/tex]
- Plug the known values and then simplify !
[tex] \large{ \tt{ ↦ \: {10}^{2} = {6}^{2} + {b}^{2} }}[/tex]
[tex] \large{ \tt{↦100 = 36 + {b}^{2} }}[/tex]
[tex] \large{ \tt{↦36 + {b}^{2} = 100 }}[/tex]
[tex] \large{ \tt{ ↦{b}^{2} = 100 - 36}}[/tex]
[tex] \large{ \tt{↦ {b}^{2} = 64}}[/tex]
[tex] \large{ \tt{↦b = \sqrt{64}}} [/tex]
[tex] \boxed{ \large{ \tt{↦ \: b = 8 \: cm}}}[/tex]
- Hence , The length of QR is 8 cm .
✺ Raise you hand and clear your doubts , the bullies at the last benches and the nerds at the first benches are not going to write your exam , it doesn't matter what class will think about you!
♡ Hope I helped! ツ
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