Question
Download Solution PDFThe 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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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