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What is the length of the hypotenuse?

What is the length of the hypotenuse?-example-1

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\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) \\⇢  ({12 \: ft})^(2) + ( {9 \: ft})^(2) = {c}^(2) \\ ⇢ 144 \: {ft}^(2) + 81 \: {ft}^(2) = {c}^(2) \\ ⇢ 225 \: {ft}^(2) = {c}^(2) \\ ⇢  \sqrt{225 \: {ft}^(2) } = c \\ ⇢  \sqrt{15 * 15 \: {ft}^(2) } = c \\ ⇢ 15 \: ft = c


\sf\blue{Therefore,\:the\:length\:of\:the\:hypotenuse\:is\:15\:feet.}


\huge\bold{To\:verify :}


( {12 \: ft})^(2) + ( {9 \: ft})^(2) = ( {15 \: ft})^(2) \\⇝144 \: {ft}^(2) + 81 \: {ft}^(2) = 225 \: {ft}^(2) \\ ⇝225 \: {ft}^(2) = 225 \: {ft}^(2) \\ ⇝L.H.S.=R. H. S

Hence verified.


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

What is the length of the hypotenuse?-example-1
User Scniro
by
8.9k points
2 votes

Answer:

h=15feet.

Explanation:

using Pythagoras theorem

h²=p²+b²

  • h²=12²+9²
  • h²=144+81
  • h=√225
  • h=15feet.

hope it helps.

stay safe healthy and happy.

User CRM
by
7.7k points

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