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The points (0,3) and (4,0) are joined to find a triangle with x-axis

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The points (0,3) and (4,0) are joined to find a triangle with x-axis  [#permalink]

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New post 21 Nov 2018, 07:04
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Question Stats:

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The points (0,3) and (4,0) are joined to find a triangle with x-axis and y-axis as the other sides of the triangle. The area of this triangle overlaps with approximately what percentage of the area of a circle with equation \(x^2 + y^2 = 25\)?

A. 4%
B. 8%
C. 12%
D. 16%
E. 20%

Source: Experts Global

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Re: The points (0,3) and (4,0) are joined to find a triangle with x-axis  [#permalink]

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New post 21 Nov 2018, 20:49
pushpitkc wrote:
The points (0,3) and (4,0) are joined to find a triangle with x-axis and y-axis as the other sides of the triangle. The area of this triangle overlaps with approximately what percentage of the area of a circle with equation \(x^2 + y^2 = 25\)?

A. 4%
B. 8%
C. 12%
D. 16%
E. 20%

Source: Experts Global



So we have two figures..
1) a triangle with sides of 3 and 4..
This is right angled triangle with X axis , y axis and the hypotenuse joining (0,3) and (4,0)
So area = (1/2)*3*4=6
2) a circle with radius 5 as the equation of circle is \(x^2+y^2=r^2=5^2\)
Since radius is 5, the entire triangle with sides 3 and 4 from the centre of circle will be completely within this circle. Area = πr^2=22*25/7=550/7

Therefore answer is 6/(550/7)*100= 600*7/550=84/11~8%

B
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Re: The points (0,3) and (4,0) are joined to find a triangle with x-axis  [#permalink]

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New post 24 Nov 2018, 01:46
pushpitkc wrote:
The points (0,3) and (4,0) are joined to find a triangle with x-axis and y-axis as the other sides of the triangle. The area of this triangle overlaps with approximately what percentage of the area of a circle with equation \(x^2 + y^2 = 25\)?

A. 4%
B. 8%
C. 12%
D. 16%
E. 20%

Source: Experts Global



Plot figure for triangle we would , area of triangle : 05*4*3= 6
Area of circle with radius 5 as eqn of circle is given : pi*25
% of area= 6*7/22*25= ~8 % IMO B
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Re: The points (0,3) and (4,0) are joined to find a triangle with x-axis  [#permalink]

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New post 24 Nov 2018, 03:13
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Area of the Triangle: \(\frac{1}{2}*3*4\)=6
Area of the Circle: \(5^2*π=25*3.14=80\) (Estimation)

Percentage are of the triangle of the area of the circle: \(\frac{6}{80}*100=7.5%\)

Answer: B
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Re: The points (0,3) and (4,0) are joined to find a triangle with x-axis   [#permalink] 24 Nov 2018, 03:13
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