Triangle is a very popular shape used in interior designing. The picture given above shows a cabinet designed by a famous interior designer.

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Class 10 CBSE Mathematics Standard Sample Paper 2024-25 question no 37 Case Study Based Question 
Triangle is a very popular shape used in interior designing. The picture given above shows a cabinet designed by a famous interior designer. Here the largest triangle is represented by △ ABC and smallest one with shelf is represented by △ DEF. PQ is parallel to EF. (i) Show that △ DPQ ∼ △ DEF.
(ii) If DP= 50 cm and PE = 70 cm then find 𝑃𝑄 𝐸𝐹 . (iii) (A) If 2AB = 5DE and △ ABC ∼ △ DEF then show that π‘π‘’π‘Ÿπ‘–π‘šπ‘’π‘‘π‘’π‘Ÿ π‘œπ‘“ △𝐴𝐡𝐢 π‘π‘’π‘Ÿπ‘–π‘šπ‘’π‘‘π‘’π‘Ÿ π‘œπ‘“ △𝐷𝐸𝐹 is constant. OR (iii) (B) If AM and DN are medians of triangles ABC and DEF respectively then prove that △ ABM ∼ △ DEN. 

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