Question

Construct a triangle similar to ΔABC in which AB = 4.6 cm, BC = 5.1 cm, ∠A = 60° with scale factor 4 : 5.

Answer 1

Given that

Construct a ΔABC of given data, AB = 4.6 cm, BC = 5.1 cm, ∠A = 60° and then a triangle similar to it whose sides are (4.5 = 4/5)^th of the corresponding sides of ΔABC.

We follow the following steps to construct the given

Step of construction

Step: I- First of all we draw a line segment AB = 4.6 cm.

Step: II- With A as centre draw an angle ∠A = 60°.

Step: III- With B as centre and radius = BC = 5.1 cm, draw an arc, intersecting the arc drawn in step II at C.

Step: IV- Joins BC to obtain ΔABC.

Step: V- Below AB, makes an acute angle ∠BAX = 60°.

Step: VI- Along AX, mark off five points A₁, A₂, A₃, A₄ and A₅ such that AA₁ = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅

Step: VII- Join A₅B.

Step: VIII- Since we have to construct a triangle each of whose sides is (4/5)^th of the corresponding sides of ΔABC.

So, we take four parts out of five equal parts on AX from point A₄ draw A₄B' || A₅B, and meeting AB at B’.

Step: IX- From B’ draw B'C' || BC and meeting AC at C’

Thus, ΔAB'C' is the required triangle, each of whose sides is (4/5)^th of the corresponding sides of ΔABC.