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Mathematics · 2026 · 5 marks
CBSE 2026 · Region 2 · Set 1 · Q34
(a) Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides…
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
As shown in the given figure, a girl of height $\displaystyle 90$ cm is walking away from the base of a lamp post at a speed of $\displaystyle 1.2$ m/s. If the lamp is $\displaystyle 3.6$ m above the ground, find the length of her shadow after $\displaystyle 4$ seconds.
Marking-scheme solution
OR
OR
from the base of a lamp post at a speed of $\displaystyle 1.2 \mathrm{~m} / \mathrm{s}$. If the lamp is
3.$\displaystyle 6$ m above the ground, find the length of her shadow after
$\displaystyle 4$ seconds.
$\displaystyle \mathrm{BD}=$ speed × time $\displaystyle =1.2 \times 4=4.8 \mathrm{~m}$
$\displaystyle \Delta \mathrm{ABE} \sim \Delta \mathrm{CDE}$
$\displaystyle \Rightarrow \frac{\mathrm{BE}}{\mathrm{DE}}=\frac{\mathrm{AB}}{\mathrm{CD}}$
$\displaystyle \Rightarrow \frac{4.8+\mathrm{DE}}{\mathrm{DE}}=\frac{3.6}{0.9}$
$\displaystyle \Rightarrow \mathrm{DE}=1.6 \mathrm{~m}$
∴ Shadow of the girl after walking for $\displaystyle 4$ seconds is $\displaystyle 1.6$ m long
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CBSE Class 10 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.