The mid points of AB and AC of a △ABC are X and Y, respectively. If BC + XY = 24 units, then the value of BC - XY is:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 1)

Answer 1

Given:

The midpoints of AB and AC of a △ABC are X and Y, respectively.

If BC + XY = 24 units

Concept used:

Mid points of a triangle forming a quadrilateral with triangle is half of the base of triangle

Calculations:

According to the question,

BC + XY = 24 ..........(1)

Since XY = 1/2 of BC,

⇒ 1/2BC + BC = 24

⇒ 3BC = 24 × 2

⇒ 3BC = 48

⇒ BC = 16 units

From Eq. (1) we get,

⇒ 16 + XY = 24

⇒ XY = 8 units

Now accordingly,

⇒ BC - XY = 16 - 8 = 8 units

∴ The value of BC - XY is 8 units.

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