Question

Construct a triangle similar to a given triangle PQR with its sides equal to `7/3` of the corresponding sides of the triangle PQR (scale factor `7/3 > 1`)

Answer 1

Given triangle ABC, we are required to construct another triangle whose sides are `7/3` of the corresponding sides of the ∆ABC.

Steps of construction:

(i) Construct a ∆PQR with any measurement.

(ii) Draw a ray QX making an acute angle with QR on the side opposite to the vertex P.

(iii) Locate 7 points Q₁, Q₂, Q₃, Q₄, Q₅, Q₆, Q₇ on QX.

So that QQ₁ = Q₁Q₂ = Q₂Q₃ = Q₃Q₄ = Q₅Q₆ = Q₆Q₇ 

(iv) Join Q₃ to R and draw a line through Q₇ parallel to Q₃ R intersecting the extended line segment QR at R’.

(v) Draw a line parallel to RP. Intersecting the extended line segment QP at P’.

∴ ∆P’QR’ is the required triangle.