[tex]\huge\bold{Given:}[/tex]
Length of the perpendicular = 6 ft.
Length of the base = 8 ft.
[tex]\huge\bold{To\:find:}[/tex]
The length of the missing side.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\longrightarrow{\purple{x\:=\:10\:feet}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
Let [tex]"x"[/tex] be the side of the hypotenuse.
Using Pythagoras theorem, we have
( Hypotenuse )² = ( Perpendicular )² + ( Base )²
[tex]\longrightarrow{\blue{}}[/tex] [tex] {x}^{2} [/tex] = ( 6 ft )² + ( 8 ft) ²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 36 ft² + 64 ft²
[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 100 ft²
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex] \sqrt{100 \: {ft}^{2} } [/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex] \sqrt{10 \times 10 \: {ft}^{2} } [/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = [tex] \sqrt{ ({10 \: ft})^{2} } [/tex]
[tex]\longrightarrow{\blue{}}[/tex] [tex]x[/tex] = 10 ft.
Therefore, the length of the missing side [tex]x[/tex] is 10 feet.
[tex]\huge\bold{To\:verify :}[/tex]
[tex]\longrightarrow{\green{}}[/tex] ( 10 ft )² = ( 6 ft )² + ( 8 ft ) ²
[tex]\longrightarrow{\green{}}[/tex] 100 ft² = 36 ft² + 64 ft²
[tex]\longrightarrow{\green{}}[/tex] 100 ft² = 100 ft²
[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]
