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Q No. 2]B Q1 and Q2
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◆◆◆◆◆step by step explanation◆◆◆◆◆
2.b.1)
Perimeter of semi circle(protracter)=108
perimeter of semicircle=1/2×2πr
perimeter=πr
【Putting value of perimeter】
108=22/7×r
108×7/22=r
34.36=r
Diameter= 2×radius
Diameter=2×34.36
Diameter=68.72cm
2.B.2)
In the triangle it is given that D is the mid-point of BC so,
BD=CD
If D is the mid-point of BC so we can carry it as median.i.e.
(ar)ABD=(ar)ADC
(ar)ABD=1/2of (ar)ABC
We know centroid divide median in ratio of 2 : 1 , As G is centroid so AG : DG = 2 : 1
Given : D is a mid point of BC so AD is median and we know median divide triangle into two equal area triangle , So
Area of ∆ ABD = Area of ∆ ACD = Area of ∆ ABC2 --- ( 1 )
We know centroid divide median in ratio of 2 : 1 , As G is centroid so AG : DG = 2 : 1
Then ,
Area of ∆ AGB = 2/3of Area of ∆ ABD , Substitute value from equation 1 we get
Area of ∆ AGB = 2/3of Area of ∆ ABC2
Area of ∆ AGB = Area of ∆ ABC3 --- ( 2 )
And
Area of ∆ BGD = 13of Area of ∆ ABD , Substitute value from equation 1 we get
Area of ∆ BGD = 1/3of Area of ∆ ABC2
Area of ∆ BGD = Area of ∆ ABC/6 --- ( 3 )
Area of ∆ BGDArea of ∆ ABD , Substitute value from equation 1 and 3 and get
Area of ∆BGDArea of ∆ ABD = Area of ∆ ABC/6Area of ∆ ABC/2 = Area of ∆ ABC/6×2/Area of ∆ ABC = 1/3
2.b.1)
Perimeter of semi circle(protracter)=108
perimeter of semicircle=1/2×2πr
perimeter=πr
【Putting value of perimeter】
108=22/7×r
108×7/22=r
34.36=r
Diameter= 2×radius
Diameter=2×34.36
Diameter=68.72cm
2.B.2)
In the triangle it is given that D is the mid-point of BC so,
BD=CD
If D is the mid-point of BC so we can carry it as median.i.e.
(ar)ABD=(ar)ADC
(ar)ABD=1/2of (ar)ABC
We know centroid divide median in ratio of 2 : 1 , As G is centroid so AG : DG = 2 : 1
Given : D is a mid point of BC so AD is median and we know median divide triangle into two equal area triangle , So
Area of ∆ ABD = Area of ∆ ACD = Area of ∆ ABC2 --- ( 1 )
We know centroid divide median in ratio of 2 : 1 , As G is centroid so AG : DG = 2 : 1
Then ,
Area of ∆ AGB = 2/3of Area of ∆ ABD , Substitute value from equation 1 we get
Area of ∆ AGB = 2/3of Area of ∆ ABC2
Area of ∆ AGB = Area of ∆ ABC3 --- ( 2 )
And
Area of ∆ BGD = 13of Area of ∆ ABD , Substitute value from equation 1 we get
Area of ∆ BGD = 1/3of Area of ∆ ABC2
Area of ∆ BGD = Area of ∆ ABC/6 --- ( 3 )
Area of ∆ BGDArea of ∆ ABD , Substitute value from equation 1 and 3 and get
Area of ∆BGDArea of ∆ ABD = Area of ∆ ABC/6Area of ∆ ABC/2 = Area of ∆ ABC/6×2/Area of ∆ ABC = 1/3
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