Question
A 5 m 60 cm high vertical pole casts a shadow $3\ m$ $20\ cm$ long. Find at the same time the height of a pole which casts a shadow 5m long.
✓
Answer
Let the height of the vertical pole be $x\ m$ and the length of the shadow by $y\ m$.
As the height of the vertical pole increases, the length of the shadow also increases in the same ratio, so it is a case of direct proportion.
We make use of the relation of the type $\frac{{{x_1}}}{{{y_1}}} = \frac{{{x_2}}}{{{y_2}}}$
Here,
$x_1= 5m$ $60\ cm = 560\ cm$
$y_1= 3m$ $20\ cm = 320\ cm$
$x_2= 5m$ $00\ cm = 500\ cm$
Therefore, $\frac{{{x_1}}}{{{y_1}}} = \frac{{{x_2}}}{{{y_2}}}$ gives
$\frac{{560}}{{320}} = \frac{{{x_2}}}{{500}}$
$\therefore$ $320x_2= 560$ $\times$ $500$
$\therefore$ ${x_2} = \frac{{560 \times 500}}{{320}}$
$\therefore$ $x_2= 875$ $cm = 8\ m\ 75\ cm$
As the height of the vertical pole increases, the length of the shadow also increases in the same ratio, so it is a case of direct proportion.
We make use of the relation of the type $\frac{{{x_1}}}{{{y_1}}} = \frac{{{x_2}}}{{{y_2}}}$
Here,
$x_1= 5m$ $60\ cm = 560\ cm$
$y_1= 3m$ $20\ cm = 320\ cm$
$x_2= 5m$ $00\ cm = 500\ cm$
Therefore, $\frac{{{x_1}}}{{{y_1}}} = \frac{{{x_2}}}{{{y_2}}}$ gives
$\frac{{560}}{{320}} = \frac{{{x_2}}}{{500}}$
$\therefore$ $320x_2= 560$ $\times$ $500$
$\therefore$ ${x_2} = \frac{{560 \times 500}}{{320}}$
$\therefore$ $x_2= 875$ $cm = 8\ m\ 75\ cm$
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