Plz solve this ques 5 and 8...plzz
Answers
5. Let the sides of ∆ be a, b and c.
Now, since the sides are doubled new sides will be 2a, 2b and 2c.
s = ( a + b + c )/2
s' = ( 2a + 2b + 2c )/2
s' = 2( a + b + c )/2
s' = a + b + c
s' / s = ( a + b + c )/( a + b + c )/2
s'/s = 2
s' = 2s
Now, we know that
∆ = √[s( s - a )( s - b )( s - c )]
∆' = √[s'( s' - 2a )( s' - 2b )( s' - 2c )]
∆' = √[2s( 2s - 2a )( 2s - 2b )( 2s - 2c )]
∆' = √[ 2s × 2( s - a ) × 2( s - b ) × 2( s - c )]
∆' = √[ 16 × s( s - a )( s - b )( s - c )
∆' = 4∆
Ratio of new triangle to that of original triangle.
∆' / ∆ = 4∆ / ∆ = 4 : 1.
Answer = 4 : 1
8. Area if triangle ABC = √[s( s - a )( s - b )( s - c )]
Where s = ( a + b + c )/2
s = ( 200 + 360 + 240 ) m / 2
= 400 m.
Hence,
= √[400( 400 - 360 )( 400 - 200 )( 400 - 240 )]
=√[40 × 10 × 40 × 1 × 40 × 5 × 40 × 4 ]
= √[ 40 × 40 × 40 × 40 × 40 × 5 ]
= 1600√200
= 22627.4 m²
1 m² = 1 / 10000 hectare = 2.26 hectare.
Area of Triangle ACD =
s = ( 240 + 400 + 320 )/2 = 480 m
= √[480( 480 - 400 )( 480 - 320 )( 480 - 240 )
= √[ 40 × 12 × 40 × 2 × 40 × 4 × 40 × 6 ]
= 1600√(24 × 24)
= 1600 × 24 = 38400 m²
No. of hectare = 3.84 m²
Since it is divided into 2 equal parts, so area of AEC = BEC = 1.92 m²
Hence, area for wheat is 2.26 hectares and area for potato and onions is 1.92 hectare.
Have great future ahead!
Answer:
(5) - 4:1
(8) - 1.92, 2.26.
Step-by-step explanation:
(5)
Let the sides be a,b,c.
⇒ Semi-perimeter (s) = (a + b + c)/2
⇒ Area of triangle = √s(s - a)(s - b)(s - c)
Given that Each side is doubled.
Sides of the new triangle is 2a,2b,2c.
Semi-perimeter of the new triangle = 2a + 2b + 2c/2
= 2(a + b + c/2
= 2s
Area of new triangle = √2s(2s - 2a)(2s - 2b)(2s - 2c)
⇒ 4√s(s - a)(s - b)(s - c)
⇒ 4 * Area of triangle.
Therefore, Ratio = 4/1
⇒ 4 : 1
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(8)
For ΔABC:
Given sides are a = 200, b = 240 m, c = 360 m.
We know that s = (a + b + c)/2
⇒ (200 + 240 + 360)/2
⇒ 400 m.
Now,
Area of triangle = √400(400 - 200)(400 - 240)(400 - 360)
= √400 * 200 * 160 * 40
= 160000√2 m^2
= 1.6 * √2 hectares.
= 2.26 hectares.
For ΔACD
Given sides are 240 m, 320 m, 400 m.
⇒ s = (a + + c)/2
= (240 + 320 + 400)/2
= 480 m.
Area of triangle ACD = √480(480 - 240)(480 - 320)(480 - 400)
= √480(240)(160)(80)
= √1474560000
= 38400 m²
= 3.84 hectares.
Therefore, Area of growing potatoes = (3.84 ÷ 2)
⇒ 1.92 hectares.
⇒ Area of growing potatoes = Area of growing onions = 1.92 hectares
⇒ Area of growing wheat = 2.26 hectares.
Hope it helps!