# Fill in the Blanks. - Mathematics

Sum

Fill in the blanks.

Point G is the centroid of  ABC.
(1) If l(RG) = 2.5 then l(GC) = _____
(2) If l(BG) = 6 then l(BQ) = _____
(3) If l(AP) = 6 then l(AG) = _____   and l(GP) = _____

#### Solution

In ∆ABC, the medians AP, BQ and CR to the sides BC, CA and AB respectively intersect at G. Since, centroid of a triangle divides the medians in the ratio of 2 : 1, then AG : GP = BG : GQ = CG : GR = 2 : 1.
(1) We have, CG : GR = 2 : 1
⇒ (GC)/(RG) = 2/1

⇒ (GC)/(2.5) = 2/1

⇒ GC = 5

(2) We have, BG : GQ = 2 : 1

⇒ (BG)/(GQ) = 2/1

⇒ (BG)/(BQ-BG) = 2/1

⇒ (6)/(BQ-6) = 2

⇒ BQ - 6 = 3

⇒ BQ = 9

(3) We have, AG : GP = 2 : 1

⇒ (AG)/(GP) = 2/1

⇒ (AG)/(AP-AG) = 2

⇒ (AG)/(6-AG) = 2

⇒ 2(6 - AG) = AG

⇒ 12 - 2AG = AG

⇒ 3AG = 12

⇒ AG = 12/3

⇒ AG = 4

Now, GP = AP − AG = 6 − 4 = 2.
Hence, we have,
(1) If l(RG) = 2.5 then l(GC) = 5
(2) If l(BG) = 6 then l(BQ) = 9
(3) If l(AP) =6 then l(AG) = 4 and l(GP) = 2

#### Notes

Concept: Altitudes of a Triangle
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#### APPEARS IN

Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 4 Altitudes and Medians of a triangle
Practice Set 4.1 | Q 7 | Page 22