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Question

Trinagles ABC and DEF are similar.
(i) If area (ΔABC)=16cm2,area(ΔDEF)=25cm2 and BC = 2.3 cm find EF.
(ii) If area (ΔABC)=9cm2,area(ΔDEF)=64cm2 and DE=5.1 cm, find AB.
(iii) If AC = 19 cm adn DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area (ΔABC)=36cm2, are (ΔDEF)=64cm2 and DE= 6.2 cm, find AB.
(v) If AB = 1.2 cm and DE=1.4 cm, find the ratio of the areas of ΔABC and ΔDEF.

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Solution

we know that the ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.
left parenthesis i right parenthesis space fraction numerator a r left parenthesis A B C right parenthesis over denominator a r left parenthesis D E F right parenthesis end fraction equals open parentheses fraction numerator B C over denominator E F end fraction close parentheses squared rightwards double arrow 16 over 25 equals open parentheses fraction numerator 2.3 over denominator E F end fraction close parentheses squared rightwards double arrow 4 over 5 equals fraction numerator 2.3 over denominator E F end fraction rightwards double arrow E F space equals space fraction numerator 2.3 cross times 5 over denominator 4 end fraction space equals 2.875 space c m
left parenthesis i i right parenthesis space fraction numerator a r left parenthesis A B C right parenthesis over denominator a r left parenthesis D E F right parenthesis end fraction equals open parentheses fraction numerator A B over denominator D E end fraction close parentheses squared rightwards double arrow 9 over 64 equals open parentheses fraction numerator A B over denominator 5.1 end fraction close parentheses squared rightwards double arrow 3 over 8 equals fraction numerator A B over denominator 5.1 end fraction rightwards double arrow A B equals space fraction numerator 5.1 cross times 3 over denominator 8 end fraction space equals 1.9125 space c m
left parenthesis i i i right parenthesis space fraction numerator a r left parenthesis A B C right parenthesis over denominator a r left parenthesis D E F right parenthesis end fraction equals open parentheses fraction numerator A C over denominator D F end fraction close parentheses squared rightwards double arrow fraction numerator a r left parenthesis A B C right parenthesis over denominator a r left parenthesis D E F right parenthesis end fraction equals open parentheses 19 over 8 close parentheses squared rightwards double arrow fraction numerator a r left parenthesis A B C right parenthesis over denominator a r left parenthesis D E F right parenthesis end fraction space equals space 361 over 64
left parenthesis i v right parenthesis space fraction numerator a r left parenthesis A B C right parenthesis over denominator a r left parenthesis D E F right parenthesis end fraction equals open parentheses fraction numerator A B over denominator D E end fraction close parentheses squared rightwards double arrow 36 over 64 equals open parentheses fraction numerator A B over denominator 6.2 end fraction close parentheses squared rightwards double arrow 6 over 8 equals fraction numerator A B over denominator 6.2 end fraction rightwards double arrow E F space equals space fraction numerator 6.2 cross times 6 over denominator 8 end fraction space equals 4.65 c m
left parenthesis v right parenthesis space fraction numerator a r left parenthesis A B C right parenthesis over denominator a r left parenthesis D E F right parenthesis end fraction equals open parentheses fraction numerator A B over denominator D E end fraction close parentheses squared rightwards double arrow fraction numerator a r left parenthesis A B C right parenthesis over denominator a r left parenthesis D E F right parenthesis end fraction equals open parentheses fraction numerator 1.2 over denominator 1.4 end fraction close parentheses squared rightwards double arrow fraction numerator a r left parenthesis A B C right parenthesis over denominator a r left parenthesis D E F right parenthesis end fraction space equals space 144 over 196 space equals space 36 over 49


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