Question

A staircase has a height of 24 ft. and a base length of 7 ft. If half height of the wall under the staircase is covered with a shelf as shown in the figure, then find x.

• A. 13 ft.
• B. 25 ft.
• C. 10 ft.
• D. 12 ft.

Answer 1

The correct option is D 12 ft.

Let 'z' be the slope of the whole staircase and 'y' be the slope of the upper half of the staircase.
Total height of the staircase = 24 ft.
Base of the staircase = 7 ft.
$\therefore z=\sqrt{{24}^2+7^2}=\sqrt{576+49}=\sqrt{625}=25ft.$
Length between the shelf and top of the staircase = 12 ft.
[$\because$ the shelf is half of the length of the staircase]
Length of the top of the shelf = 5 ft.
$\therefore y=\sqrt{{12}^2+5^2}=\sqrt{144+25}=\sqrt{169}=13ft.$
$\therefore x=z-y=25-13=12ft.$