Question

2
Use the Pythagorean Theorem (a + b² = c) to find the missing side length.

Answer 1

`\huge\bold{Given:}`

Length of the base "b" = 17 yd.

Length of the perpendicular "a" = 13 yd.
`\huge\bold{To\:find:}`

The length of the missing side, hypotenuse ("c").

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

`\boxed{C.\:21.4\:yd}` ✅

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

Using Pythagoras theorem, we have

`({perpendicular})^(2) + ({base})^(2) = ({hypotenuse})^(2) \\ \\⇢( {13 \: yd})^(2) + ( {17 \: yd})^(2) = {c}^(2) \\ \\⇢ {c}^(2) = 169 \: {yd}^(2) + 289 \: {yd}^(2) \\ \\⇢c = \sqrt{458 \: {yd}^(2) } \\ \\⇢c = 21.40 \: yd`

`\sf\blue{Therefore,\:the\:length\:of\:the\:missing\:side\:`

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

`( {13 \: yd})^(2) + ( {17 \: yd})^(2) = {21.4 \: {yd}^(2) }\\ \\ ⇝169 \: {yd}^(2) + 289 \: {yd}^(2) = 457.96 \: {yd}^(2) \\ \\⇝458 \: {yd}^(2) = \: 458\: {yd}^(2) \\\\⇝ L.H.S.=R. H. S`

Hence verified. ✔

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

Answer 2

21.4

Explanation:

`a^(2) + b^(2) = c^(2) \\13^(2) + 17^(2) = c^(2) \\169+ 289 = \sqrt{c^(2) } \\√(458) = \sqrt{c^(2) } \\21.4 = c`