Question

Anyone have the answer for this

Answer 1

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

✎ The length of the hypotenuse.

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

$\sf\purple{The\:length\:of\:the\:hypotenuse \:"c"\:is\:5.10\:km.}$

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

Using Pythagoras theorem, we have

$( {perpendicular})^{2} + ( {base})^{2} = ( {hypotenuse})^{2} \\ ⇢ ( {5 \: km})^{2} + ( {1 \: km})^{2} = ( {c})^{2} \\ ⇢ 25 \: {km}^{2} + 1 \: {km}^{2} = {c}^{2} \\ ⇢ 26 \: {km}^{2} = {c}^{2} \\ ⇢ \sqrt{26 \: {km}^{2} } = c \\ ⇢5.0990 \: km = c \\ ⇢5.10 \: km = c$

$\sf\blue{Therefore,\:the\:length\:of\:the\:hypotenuse\:is\:5.10\:km.}$

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

$( {5 \: km})^{2} + ( {1 \: km})^{2} = ( {5.10 \: km})^{2} \\ ⇝25 \: {km}^{2} + 1 \: {km}^{2} = 26 \: {km}^{2} \\ ⇝26 \: {km}^{2} = 26\: {km}^{2} \\ ⇝L.H.S.=R. H. S$

Hence verified.

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

Answer 2

The answer is radical 26. Since the triangle is right (given) you can use Pythagorean’s theorem (a^2+b^2=c^2) so in this case: c^2= 1+25=26 and you square root both sides to get rid of the ^2 and you get radical 26.