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.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 37.5.
DE || BC and DE = 1/2 × BC
It means that ADE is similar to ABC
one can say that ADE is also an equilateral triangle.
AD = AE and BD = CE.
AD + CE + BC = 30
AD + BD + BC = 30
AB + BC = 30
BC = 15
DE = 15/2 = 7.5
AB = BC = AC = 15
AD = 1/2 × AB = 15/2 = 7.5
Perimeter of BCED = 15 + 7.5 + 7.5 + 7.5 = 37.5.