Question

What is the length of the hypotenuse?

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) \\⇢  ({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.}}}}}∘`

Answer 2

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.