Question

Find the missing length in the right triangle.

Answer 1

`\huge\bold{Given:}`

Length of the perpendicular = 6 ft.

Length of the base = 8 ft.

`\huge\bold{To\:find:}`

The length of the missing side.

`\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}`

`\longrightarrow{\purple{x\:=\:10\:feet}}`

`\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}`

Let
be the side of the hypotenuse.

Using Pythagoras theorem, we have

( Hypotenuse )² = ( Perpendicular )² + ( Base )²

`\longrightarrow{\blue{}}`
`{x}^(2)` = ( 6 ft )² + ( 8 ft) ²

`\longrightarrow{\blue{}}`
`{x}^(2)` = 36 ft² + 64 ft²

`\longrightarrow{\blue{}}`
`{x}^(2)` = 100 ft²

`\longrightarrow{\blue{}}`
`x` =
`\sqrt{100 \: {ft}^(2) }`

`\longrightarrow{\blue{}}`
`x` =
`\sqrt{10 * 10 \: {ft}^(2) }`

`\longrightarrow{\blue{}}`
`x` =
`\sqrt{ ({10 \: ft})^(2) }`

`\longrightarrow{\blue{}}`
`x` = 10 ft.

Therefore, the length of the missing side
`x` is 10 feet.

`\huge\bold{To\:verify :}`

`\longrightarrow{\green{}}` ( 10 ft )² = ( 6 ft )² + ( 8 ft ) ²

`\longrightarrow{\green{}}` 100 ft² = 36 ft² + 64 ft²

`\longrightarrow{\green{}}` 100 ft² = 100 ft²

`\longrightarrow{\green{}}` L.H.S. = R. H. S.

Hence verified. ✔

`\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{☂}}}}}`