Question

For the following right triangle, find the side length x . Round your answer to the nearest hundredth.

Answer 1

`\huge\bold{Given:}`

Length of the base = 9

Length of the hypotenuse = 16
`\huge\bold{To\:find:}`

✎ The length of the perpendicular ''
`x`".

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

The length of the perpendicular
`x` is
`\boxed{±13.229}`.

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

Using Pythagoras theorem, we have

`({perpendicular})^(2) + ({base})^(2) = ({hypotenuse})^(2) \\ ⇢ {x}^(2) + {(9})^(2) = ({16})^(2) \\ ⇢ {x}^(2) + 81 = 256 \\ ⇢ {x}^(2) = 256 - 81 \\ ⇢x = √(175) \\ ⇢x = ±13.229`

`\sf\blue{Therefore,\:the\:length\:of\:the\:perpendicular \:`

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

`( {13.229})^(2) + ({9})^(2) = ({16})^(2) \\ ⇢ 175 + 81 = 256 \\ ⇢ 256 = 256 \\⇢  L.H.S.=R. H. S`

Hence verified. ✔

`\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘`