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 \:`

`\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.