Question

Look at the figure above. This is a staircase consisting of 5 steps. The height of each in-step(green area) is 6 cms.

(i) What is the total length of the pink line if the breadth of each step is 32 cms.

(ii) Write the ratio of the height of the instep to its total length of the pink line in the form of a fraction.

(iii) What fraction is the ratio of the area of the surface facing each step to the total area of the surface facing steps of the staircase in the fraction form.
[4 MARKS]

Answer 1

Concept: 1 Mark
Application:1 Mark each

(i) Given: The height of the staircase = 6 cms

The breadth of the staircase = 32 cms



So, length of the pink line will be = (breadth + height) of five steps.
$\Rightarrow$5 (6 cms) + 5 (32 cms)

$\Rightarrow 5[6+32]cms$

$\Rightarrow 5\left[38\right]cms$

$\Rightarrow 190cms$

(ii) $\frac{Thetotallengthofthein-step}{Thetotallengthofthepinkline}$

$\Rightarrow \frac{5\left(6\right)cms}{190cms}$

$\Rightarrow \frac{30}{190}\Rightarrow \frac{3}{19}$

(iii) The area of each step $=l\times b$

$=40\times 32$

$=1280c{m}^2$

and Area of 5 steps $=5\times 1280c{m}^2$

$\therefore \frac{Areaofeachstep}{Totalareaoffivesteps}$

$\Rightarrow \frac{1280c{m}^2}{5\times 1280c{m}^2}$

$\frac{1}{5}$