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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 2 · Set 2 · Q11
The sum of two numbers is 34. If $\displaystyle 3$ is subtracted from one number and $\displaystyle 2$ is added to another, the product of these two numbers becomes 260. Find the numbers.The hypotenuse (in cm) of a right angled triangle is $\displaystyle 6$ cm more than twice the length of the shortest side. If the length of third side is $\displaystyle 6$ cm less than thrice the length of shortest side, then find the dimensions of the triangle.
The sum of two numbers is 34. If $\displaystyle 3$ is subtracted from one number and $\displaystyle 2$ is added to another, the product of these two numbers becomes 260. Find the numbers.
The hypotenuse (in cm) of a right angled triangle is $\displaystyle 6$ cm more than twice the length of the shortest side. If the length of third side is $\displaystyle 6$ cm less than thrice the length of shortest side, then find the dimensions of the triangle.
Marking-scheme solution
Let the shortest side be \(\displaystyle x \mathrm{~cm}\)
\[\left.\therefore \begin{array}{l}
\text { Hypotenuse is } 2 x+6 \mathrm{~cm} \\
\text { and other side is } 3 x-6 \mathrm{~cm}
\end{array}\right\}
\]
Hence
\[\left.\begin{array}{l}
\quad(2 x+6)^{2}=x^{2}+(3 x-6)^{2} \\
\Rightarrow 6 x^{2}-60 x=0
\end{array}\right\}
\]
\[\Rightarrow x=10
\]
Dimensions of the triangle are $\displaystyle 10$ cm, $\displaystyle 24$ cm and $\displaystyle 26$ cm.
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CBSE Class 10 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.