How i solve the important question from the chapter Triangles of exercise 6.4, It is very important for the board exam so please help to solve this problem Let ΔABC ~ ΔDEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.

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# Let ΔABC ~ ΔDEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC. Q.1

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Given, ΔABC ~ ΔDEF,

Area of ΔABC = 64 cm

^{2}Area of ΔDEF = 121 cm

^{2}EF = 15.4 cm

As we know, if two triangles are similar, ratio of their areas are equal to the square of the ratio of their corresponding sides,

= AC

^{2}/DF^{2}= BC^{2}/EF^{2}∴ 64/121 = BC

^{2}/EF^{2}⇒ (8/11)

^{2}= (BC/15.4)^{2}⇒ 8/11 = BC/15.4

⇒ BC = 8×15.4/11

⇒ BC = 8 × 1.4

⇒ BC = 11.2 cm