Question

Find the missing side of this right triangle. Х 8 16 x = = [?] Enter the number that belongs in the green box. Enter​

Answer 1

`\huge\bold{Given:}`

Length of the perpendicular = 8

Length of the hypotenuse = 16

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

The length of the missing side ''
`x`".

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

`\longrightarrow{\purple{x\:=\:√192}}`

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

Using Pythagoras theorem, we have

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

`\longrightarrow{\blue{}}` (8)² +
`{x}^(2)` = (16)²

`\longrightarrow{\blue{}}` 64 +
`{x}^(2)` = 256

`\longrightarrow{\blue{}}`
`{x}^(2)` = 256 - 64

`\longrightarrow{\blue{}}`
`{x}^(2)` = 192

`\longrightarrow{\blue{}}`
`x` =
`√(192)`

Therefore, the length of the missing side
`x` is
`√(192)`.

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

`\longrightarrow{\green{}}` (8)² + (√192)² = (16)²

`\longrightarrow{\green{}}` 64 + 192 = 256

`\longrightarrow{\green{}}` 256 = 256

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

Hence verified. ✔

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