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Mathematics · 2025 · 5 marks
CBSE 2025 · Region 1 · Set 1 · Q34
(a) The perimeter of a right triangle is 60 cm and its hypotenuse is 25 cm. Find the lengths of other two sides of the triangle.
(a)
The perimeter of a right triangle is $\displaystyle 60$ cm and its hypotenuse is $\displaystyle 25$ cm. Find the lengths of other two sides of the triangle.
OR
(b)
A train travels a distance of $\displaystyle 480$ km at a uniform speed. If the speed had been $\displaystyle 8$ km/h less, then it would have taken $\displaystyle 3$ hours more to cover the same distance. Find the speed of the train.
Marking-scheme solution
Let the other two sides be x cm and y cm ATQ
\[\begin{aligned}
& x+y+25=60 \\
& y=35-x
\end{aligned}
\]
Now,
\[\left.\begin{array}{l}
x^{2}+y^{2}=(25)^{2} \\
x^{2}+(35-x)^{2}=625 \\
x^{2}-35 x+300=0 \\
(x-20)(x-15)=0 \\
\Rightarrow x=20,15 \\
x=20 \Rightarrow y=15 \\
x=15 \Rightarrow y=20
\end{array}\right\}
\]
Hence sides are $\displaystyle 15$ cm and $\displaystyle 20$ cm.
Let the speed of train be x km/h Reduced speed of train \(\displaystyle =(\mathrm{x}-8) \mathrm{km} / \mathrm{h}\)
ATQ
\[\frac{480}{x-8}-\frac{480}{x}=3
\]
\[\begin{aligned}
& x^{2}-8 x-1280=0 \\
& (x-40)(x+32)=0 \\
& \Rightarrow x=40
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.