Q. 30

The perimeters of

Answer :

Ξ”ABC~Ξ”DEF


π‘ƒπ‘’π‘Ÿπ‘–π‘šπ‘’π‘‘π‘’π‘Ÿ (Δ𝐴𝐡𝐢)/π‘ƒπ‘’π‘Ÿπ‘–π‘šπ‘’π‘‘π‘’π‘Ÿ (Δ𝐷𝐸𝐹) = (𝐴𝐡+𝐡𝐢+𝐢𝐴)/(𝐷𝐸+𝐸𝐹+𝐹𝐷) = 𝐴𝐡/𝐷𝐸


25/15=9/𝑋


x = 5.4cm


DE = 5.4cm


OR



Construction-Draw AM βŠ₯ BC


BD = 1/3 BC (Given), BM = 1/2 BC (as AM acts as median)


In Ξ”ABM,


AB2 = AM2 + BM2 (By Pythagoras theorem)


= AM2 + (BD + DM)2


=AM2 + DM2 + BD2 + 2BD.DM


=AD2 + BD2 + 2BD(BM - BD)


=AD2 + (BC/3)2 + 2.BC/3.(BC/2 - BC/3)


=AD2 + 2BC2/9


=AD2 + 2AB2/9 (AB = Bc, equilateral triangle)


Multiply the equation by 9,


9AB2 = 9AD2 + 2AB2


Hence,7AB2 = 9AD2


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Heights and Distances - IHeights and Distances - IHeights and Distances - I54 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

In Fig. 3,<Mathematics - Board Papers

In an equilateralRD Sharma - Mathematics