Triangle ABC is an equilateral triangle D and E are points on AB and AC respectively such that DE is...........

Quantitative Aptitude (CGL) Geometry

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.

This questions was previously asked in

SSC CGL 20th August 2021 Shift-1

37.5

Let’s break down the problem:

- Let side of equilateral triangle ABC = x.

- DE is parallel to BC and DE = ½ BC = ½x.

- By similarity, triangles ADE ~ ABC, so ratio of sides is ½.

- Thus, AD = ½ AB = ½x and AE = ½ AC = ½x.

- Given: AD + CE + BC = 30

AD = ½x

BC = x

CE = EC = AC - AE = x - ½x = ½x

So, ½x + ½x + x = 30 ? 2x = 30 ? x = 15

- Find perimeter of quadrilateral BCED: BC + CE + ED + DB

BC = 15

CE = 7.5

ED = 7.5 (since DE = ½x)

DB = AB - AD = x - ½x = 7.5

So, Perimeter = 15 + 7.5 + 7.5 + 7.5 = 37.5 cm

- Option 1: 37.5 (Correct Answer)

- Option 2: 25 (Too small, neglects full lengths)

- Option 3: 45 (Too large, exceeds total segments)

- Option 4: 35 (Close, but not exact)

Submit Error