Question

Find the length of the third side. If necessary, round to the nearest tenth

Answer 1

$\huge\bold{Given:}$

Length of the base = 8

Length of the hypotenuse = 17

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

The length of the third side ''$x$".

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

$\longrightarrow{\purple{x\:=\: 15}}$ 

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

Using Pythagoras theorem, we have

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

$\longrightarrow{\blue{}}$ ${x}^{2}$ + (8)² = (17)²

$\longrightarrow{\blue{}}$ ${x}^{2}$ + 64 = 289

$\longrightarrow{\blue{}}$  ${x}^{2}$ = 289 - 64

$\longrightarrow{\blue{}}$  ${x}^{2}$ = 225

$\longrightarrow{\blue{}}$  $x$ = $\sqrt{225}$

$\longrightarrow{\blue{}}$  $x$ = $15$

Therefore, the length of the missing side $x$ is $15$.

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

$\longrightarrow{\green{}}$ (15)² + (8)² = (17)²

$\longrightarrow{\green{}}$ 225 + 64 = 289

$\longrightarrow{\green{}}$ 289 = 289

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

Hence verified.

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