wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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.

Open in App
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


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Areas of Similar Triangles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon