CBSE Class 10 Mathematics Standard 2025: question 32

Hints

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Step-by-step solution

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1. Let each equal side be $x$ cm and the base be $y$ cm.

   Perimeter: $x+x+y=32\Rightarrow 2x+y=32$ …(1)

   1 mark

2. Given condition: $x=\frac{5}{6}y$ …(2)

   1 mark

3. Substitute (2) in (1): $\frac{5}{3}y+y=32\Rightarrow \frac{8}{3}y=32\Rightarrow y=12$, and $x=\frac{5}{6}\times 12=10$.

   So the sides are 10 cm, 10 cm and 12 cm.

   1 mark

4. Semi-perimeter: $s=\frac{32}{2}=16$ cm

   ½ mark

5. By Heron's formula:

   Area $=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{16\times 6\times 6\times 4}$

   1 mark

6. $=\sqrt{2304}=48{\text{ cm}}^2$

   ½ mark

Answer: Area = 48 cm²

Revise the chapter

• Chapter: Triangles (notes, formulas, where marks are lost and every past question)