Triangle ABC is an equilateral triangle. D and E are points on AB and AC respectively such that DE is parallel to BC and is equal to half the length of BC. If AD + CE + BC = 30 cm, then find the perimeter (in cm) of the quadrilateral BCED.

37.5

AD + CE + BC = 30 cm

Since,

\(\Delta \)ABC is an equilateral triangle so AB = AC = BC

and D and E are midpoints of AB and AC respectively.

= AD = AE and DB = EC

AD + DB + BC = 30

= AB + BC = 30

= 2AB = 30

= AB = 15

Hence,

= AB = BC = CA = 15 and

= AD = DB = AE = EC = DE = \(\frac{15}{2}\) = 7.5

Now,

The perimeter of the quadrilateral BCED,

= BC + CE + ED+ BD = 15 + 7.5 + 7.5 + 7.5 = 37.5

Therefore, the perimeter of the quadrilateral BCED is 37.5.