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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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21 Nov 2018, 07:04
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Difficulty:

55% (hard)

Question Stats:

53% (02:07) correct 47% (02:11) wrong based on 72 sessions

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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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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

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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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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24 Nov 2018, 03:13
1
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: $$\frac{6}{80}*100=7.5%$$

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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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