Question

A book that is 13 inches tall is leaning against the edge of a wall. If the bottom of the book is 5 inches from the wall, how far up the wall is the top of the book?

Answer 1

`\huge\bold{Given:}`

Length of the book (hypotenuse) = 13 inches

Distance of the book from the foot of the wall (base) = 5 inches

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

Length of the book on the wall (perpendicular ''
`x`").

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

`\longrightarrow{\purple{x\:=\:12\:inches}}`

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

By Pythagoras theorem, we have

(Perpendicular)² + (Base)² = (Hypotenuse)²

`\longrightarrow{\blue{}}`
`{x}^(2)` + (5 in) ² = (13 in)²

`\longrightarrow{\blue{}}`
`{x}^(2)` + 25 in² = 169 in²

`\longrightarrow{\blue{}}`
`{x}^(2)` = 169 in² - 25 in²

`\longrightarrow{\blue{}}`
`{x}^(2)` = 144 in²

`\longrightarrow{\blue{}}`
`x` =
`\sqrt{144 \: {in}^(2) }`

`\longrightarrow{\blue{}}`
`x` =
`\sqrt{12 * 12 \: {in}^(2) }`

`\longrightarrow{\blue{}}`
`x` =
`\sqrt{ ({12 \: in})^(2) }`

`\longrightarrow{\blue{}}`
`x` = 12 in

Therefore, the height of the book on the wall
`x` is 12 inches.

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