Question

Find the side length x

Answer 1

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

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

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

`\sf\purple{The\:length\:of\:the\:hypotenuse \:`

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

Using Pythagoras theorem, we have

`( {hypotenuse})^(2) = ( {perpendicular})^(2) + ( {base})^(2) \\ ⇢ {x}^(2) = {6}^(2) + {8}^(2) \\ ⇢ {x}^(2) = 36 + 64 \\ ⇢ {x}^(2) = 100 \\ ⇢ x = √(100) \\ ⇢x = √(10 * 10) \\ ⇢x = \sqrt{ ({10})^(2) } \\ ⇢x = 10`

`\sf\blue{Therefore,\:the\:length\:of\:the\:hypotenuse\:is\:10.}`

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

`{x}^(2) = {6}^(2) + {8}^(2) \\⇝ ({10})^(2) = 36 + 64 \\ ⇝10 * 10 = 100 \\ ⇝100 = 100 \\ ⇝L.H.S.=R. H. S`

Hence verified. ✔

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

Answer 2

x = 10

Explanation:

8² + 6² = x²

64 + 36 = x

64 + 36 = 100

√100 = 10