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27 Oct 2021, 07:15
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E
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Difficulty:
35%
(medium)
Question Stats:
78% (02:31) correct
22%
(02:37)
wrong
based on 273
sessions
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What is the area of shaded region in the figure shown?
A. 4/3
B. 8/3
C. 4
D. 8
E. 12
Attachment:
1.gif [ 3.57 KiB | Viewed 6514 times ]
27 Oct 2021, 12:26
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Bunuel
y=4 means that this line is parallel to x axis. Therefore, \(\triangle OPQ\) is similar to \(\triangle RSQ\) as shown in the sketch attached.
Similar triangles have areas in the ratio of square of their sides. ratio of areas of \(\triangle OPQ\):\(\triangle RSQ\)=\(OQ^2:SQ^2=1^2:3^2=1:9\)
Area of \(\triangle OPQ\) = \(\frac{1}{2}*\frac{8}{3}*1=\frac{4}{3}\)
Area of \(\triangle RSQ\) = 9* Area of \(\triangle OPQ\) = \(9*\frac{4}{3}\) = \(12\)
E
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1.gif [ 5.49 KiB | Viewed 6226 times ]
General Discussion
12 Nov 2021, 04:02
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We know 2 points on the line - (-8/3,0) and (0,1)
Equation of the line:\( y = mx + b\)
m = 1- 0/0 - (-8/3)
m = \(\frac{3}{8}\)
It is clear from the diagram that b = 1.
So, y = 3x/8 + 1
When y = 4,
4 = 3x/8 + 1
32 = 3x + 8
x = 8
The coordinates of the point on the right hand side are (8,4)
Now we know 2 coordinates of the triangle. The base and the height will measure 3 and 8.
Therefore, area of triangle = \(\frac{1}{2} * b * h\)
= \(\frac{1}{2} * 3 * 8\)
= 12
Equation of the line:\( y = mx + b\)
m = 1- 0/0 - (-8/3)
m = \(\frac{3}{8}\)
It is clear from the diagram that b = 1.
So, y = 3x/8 + 1
When y = 4,
4 = 3x/8 + 1
32 = 3x + 8
x = 8
The coordinates of the point on the right hand side are (8,4)
Now we know 2 coordinates of the triangle. The base and the height will measure 3 and 8.
Therefore, area of triangle = \(\frac{1}{2} * b * h\)
= \(\frac{1}{2} * 3 * 8\)
= 12
