Question

A $25-foot$ ladder leans against a building. As the bottom of he ladder at point A slides away from the building, the top of the ladder, B, slides from a height of $24$ feet above the ground to a height of $16$ feet. How many feet did the bottom of the ladder slide?

• A. $7$
• B. $8$
• C. $9$
• D. $12.2$
• E. $19.2$

Answer 1

Answer: (D)

$12.2$

In $△ABC$

$A{B}^2=B{C}^2-A{C}^2$

$\Rightarrow A{B}^2=(25{)}^2-(24{)}^2$

$\Rightarrow A{B}^2=625-576$

$\Rightarrow A{B}^2=49$

$\Rightarrow AB=\sqrt{49}$

$\Rightarrow AB=7$

When ladder slides from the height of $24$ feet to height of $16$ feet then the new position of the ladder on the bottom is point $E$

$\therefore △ADE$

$A{E}^2=D{E}^2-A{D}^2$

$\Rightarrow A{E}^2=(25{)}^2-(16{)}^2$

$\Rightarrow A{E}^2=625-256$

$\Rightarrow A{E}^2=369$

$\Rightarrow AE=\sqrt{369}$

$\Rightarrow AE=19.2$

$\therefore$ the bottom of the ladder slide $=$ $AE-AB=19.2-7=12.2$