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

Question

asked Oct 25, 2022 21.1k views

1 Answer

Yantrab · Answer 1 · 2022-10-30T02:29:09+0000

$\huge\bold{Given:}$

Length of the perpendicular = 8

Length of the hypotenuse = 16

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

The length of the missing side ''
".

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

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

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

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

$\longrightarrow{\blue{}}$
=
√(192)

Therefore, the length of the missing side
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. ✔

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