Mathematics
In the given figure, D, E, F are the mid-points of the sides BC, CA and AB respectively.
(i) If AB = 6.2 cm, find DE
(ii) If DF = 3.8 cm, find AC
(iii) If perimeter of △ABC is 21 cm, find FE
Mid-point Theorem
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Answer
By mid-point theorem,
The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
(i) Since, E and D are the mid-points of AC and BC respectively.
By mid-point theorem,
⇒ DE = × 6.2 = 3.1 cm
Hence, DE = 3.1 cm.
(i) Since, F and D are the mid-points of AB and BC respectively.
⇒ DF = AC
⇒ AC = 2 × 3.8
⇒ AC = 7.6 cm
Hence, AC = 7.6 cm.
(iii) From above,
AC = 7.6 cm, AB = 6.2 cm
Given,
Perimeter of △ABC = 21 cm
⇒ AB + AC + BC = 21
⇒ 6.2 + 7.6 + BC = 21
⇒ BC + 13.8 = 21
⇒ BC = 21 - 13.8
⇒ BC = 7.2 cm
Since, F and E are the mid-points of AB and AC respectively.
⇒ FE = BC
⇒ FE = × 7.2
⇒ FE = 3.6 cm
Hence, FE = 3.6 cm.
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