Draw a triangle with sides 5 cm, 6 cm and 7 cm. Then construct another triangle whose sides are 2/3 times the corresponding sides of the first triangle.

Given,

PQ = 5 cm

QR = 7 cm

RP = 6 cm

Steps for construction;

(i) Draw a line QR of 7 cm.

(ii) Taking point R as center draw an arc with any radius

(iii) With the same radius draw an arc on the previous arc.

(iv) Draw a line from the point where both the arc intersect each other

(v) Taking a length of 6 cm mark a point P o the line.

(vi) Now taking Q as center draw a line joining point P.

(vii) Draw a ray X from the point Q and mark 3 points Q₁, Q₂ and Q₃ on the ray.

(viii) Join Q₃ to point R and Q₂ to a point R’ on the line QR. As we can see Q₃R and Q₂R’ are parallel.

(ix) Draw a parallel line to RP and mark the point as P’.

(x) A triangle P’QR’ is formed

So, we get the desired ∆P’QR’.

And ratio is 2/3 times of corresponding sides.