D and E are respectively the points on sides AB and AC of triangle ABC such that AE = 5cm - Maths - Triangles

Question

D and E are respectively the points on sides AB and AC of
triangle ABC such that AE = 5cm , AC = 7 5cm , DE = 4 2cm and DE is
parallel to BC Then find the length of BC

Manbar Singh · Accepted Answer

We have ABC as the given ∆ in which DE∥BC
Now, AE = 5 cm ; AC = 7
5 cmSo, EC = 7
5 cm - 5 cm = 2
5 cmDE = 4
2 cm  ;  BC = ?Since DE∥BC and AB is a transversal, then∠ADE = ∠ABC  corresponding anglesSince DE∥BC and AC is a transversal, then∠AED = ∠ACB  corresponding anglesnow,In ∆ADE and ∆ABC, ∠ADE = ∠ABC  proved above∠AED = ∠ACB  proved aboveso, ∆ADE ~ ∆ABC   AA similarity⇒ADAB = DEBC = AEAC  correponding sides of similar ∆'s are proportional⇒DEBC = AEAC⇒4
2BC = 57 5⇒BC = 7 5 × 4
25 = 1 5 × 4 2 = 6 3 cm

D and E are respectively the points on sides AB and AC of triangle ABC such that AE = 5cm , AC = 7.5cm , DE = 4.2cm and DE is parallel to BC . Then find the length of BC