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.
Answer & explanation
Correct answer: option 1
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.