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

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

$\sf\blue{Therefore,\:the\:length\:of\:the\:perpendicular \:"x"\:is\:±13.229.}$

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

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

Hence verified. ✔

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