Question

∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1 cm, ∠B = 40° , BC = 4.8 cm, AC/LN = 4/7 .Construct ∆ABC and ∆LBN.

Answer 1

Analysis:

As shown in the figure,

Let B – C – N and B – A – L.

      Rough Fighure

∆ABC ~ ∆LBN …[Given] 

 ∴ ∠ABC ≅ ∠LBN …[Corresponding angles of similar triangles] 

AB/LB = BC/CN  = AC/LN  …(i)[Corresponding sides of similar triangles] 

But. = AC/LN  = 4/7 …(ii)[Given] 

∴ AB/LB = BC/CN = AC/LN = 4/7  …[From(i)and(ii)] 

∴ sides of ∆LBN are longer than corresponding sides of ∆ABC. 

∴ If seg BC is divided into 4 equal parts, then seg BN will be 7 times each part of seg BC.

So, if we construct ∆ABC, point N will be on side BC, at a distance equal to 7 parts from B. 

Now, point L is the point of intersection of ray BA and a line through N, parallel to AC. 

∆LBN is the required triangle similar to ∆ABC.

Steps of construction: 

i. Draw ∆ABC of given measure. Draw ray BD making an acute angle with side BC. 

ii. Taking convenient distance on compass, mark 7 points B₁ , B₂, B3 , B₄ , B₅ , B₆ and B7 such that 

BB₁ = B₁ B₂ = B₂ B₃ = B₃B₄ = B₄ B₅ = B₅ B₆ = B₆B_7.

iii. Join B₄ C. Draw line parallel to B₇ C through B to intersects ray BC at N. 

iv. Draw a line parallel to side AC through N. Name the point of intersection of this line and ray BA as L. 

∆LBN is the required triangle similar to ∆ABC.