[tex]\huge\bold{Given:}[/tex]
Length of the perpendicular = 3
Length of the hypotenuse = 6
[tex]\huge\bold{To\:find:}[/tex]
The value of ''[tex]x[/tex]".
[tex]\huge\bold{Solution:}[/tex]
[tex]\longrightarrow{\purple{A.\:x\:=\:√27}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
Using Pythagoras theorem, we have
( Perpendicular )² + ( Base )² = (Hypotenuse)²
[tex]\longrightarrow{\blue{}}[/tex] ( 3 )² + [tex]{x}^{2}[/tex] = ( 6 )²
[tex]\longrightarrow{\blue{}}[/tex] 9 + [tex]{x}^{2}[/tex] = 36
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 36 - 9
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 27
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex]\sqrt{27}[/tex]
Therefore, the length of the missing side [tex]"x"[/tex] is [tex]\sqrt{27}[/tex].
[tex]\huge\bold{To\:verify :}[/tex]
[tex]\longrightarrow{\green{}}[/tex] ( 3 )² + ( √27 )² = ( 6 )²
[tex]\longrightarrow{\green{}}[/tex] 9 + 27 = 36
[tex]\longrightarrow{\green{}}[/tex] 36 = 36
[tex]\longrightarrow{\green{}}[/tex] L. H. S. = R. H. S.
Hence verified. ✔
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
