Ex 6.4, 1

Transcript

Ex 6.4, 1 Let ΔABC ~ ΔDEF and their areas be, respectively, 64 cm2 and 121 cm2 . If EF = 15.4cm, find BC. Given:- ΔABC ~ ΔDEF ar ΔABC = 64 cm2 ar ΔDEF = 121 cm2 EF = 15.4 cm To find : BC Solution :- Since ΔABC ~ ΔDEF We know that if two triangle are similar , Ratio of areas is equal to square of ratio of its corresponding sides Hence, (𝑎𝑟 ∆ 𝐴𝐵𝐶)/(𝑎𝑟 ∆ 𝐷𝐸𝐹)=(𝐵𝐶/𝐸𝐹)^2 Putting the values 64/121=(𝐵𝐶/15.4)^2 64/121=𝐵𝐶2/(15.4)2 64/121×(15.4)2=𝐵𝐶2 ((8 × 8)/(11 × 11))×(15.4)2=𝐵𝐶2 82/112×(15.4)2=𝐵𝐶2 (8/11×15.4)2=𝐵𝐶2 8/11×15.4=𝐵𝐶 BC = 8/11×15.4 BC = 8×1.4 BC = 11.2 Hence, BC = 11.2 cm