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Line parallel to the base cuts off a given fraction of the area: find the segment

This type of question, asked 2 times: CDS 2 2017, CDS 2 2022. All 2 questions below, oldest first.

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  1. Question 1

    CDS 2 2017

    82
    One-fifth of the area of a triangle ABC is cut off by a line DE drawn parallel to BC such that D is on AB and E is on AC. If BC = 10 cm, then what is DE equal to ?

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  2. Question 2

    CDS 2 2022

    100
    In a triangle ABC, DE is a line segment which intersects AB at D and AC at E such that DE is parallel to BC. The line segment divides the triangle in two parts of equal area. What is BDAB\frac{BD}{AB} equal to ?

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