Question
Download Solution PDFThe perimeter of two similar triangles ΔABC and ΔPQR is 24 cm and 21 cm respectively. If the area of ΔABC is 448 cm2, find the area of the ΔPQR.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFor two similar triangles, the corresponding sides are in proportion and the ratio of the perimeter of the triangles is equal to the ratio of sides
Also, the ratio of the areas of the similar triangles is equal to the square of the ratio of their corresponding sides
⇒ Ratio of areas of similar triangles = Square of ratio of perimeter of triangles
⇒ Area of ΔABC/Area of ΔPQR = (Perimeter of ΔABC/Perimeter of ΔPQR)2
⇒ 448/Area of ΔPQR = (24/21)2
⇒ Area of ΔPQR = 49/64 × 448
∴ Area of ΔPQR = 343 cm2Last updated on Jun 19, 2025
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