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Subject Test Math 2

Question 6 of 28

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SAT Subject Test

In the x y-plane, what is the area of a triangle whose vertices are left parenthesis square root of 2 end root comma 0 right parenthesis, left parenthesis 2 comma square root of 10 end root right parenthesis, and left parenthesis 5 comma 0 right parenthesis?

Select an Answer

3.59

Correct Answer: 
No

5.67

Correct Answer: 
Yes

7.91

Correct Answer: 
No

11.18

Correct Answer: 
No

11.34

Correct Answer: 
No

It is helpful to draw a sketch of the triangle:

The graph shows a triangle in the x y plane with origin labeled O. There are equally spaced tick marks on the x- and y-axes, and number 1 is labeled on both axes. The triangle has its base lying on the x-axis, and the vertex opposite the base is above the x-axis. Of the three vertices, one is slightly more than 3 tick marks above the x-axis and 2 tick marks to the right of the y-axis, and the other two vertices are on the x-axis with one vertex slightly more than 1 tick mark to the right of origin O, and the other vertex 5 tick marks to the right of origin O.

The length of the base of the triangle is 5 minus square root of 2 end root and the height of the triangle is square root of 10 end root. Therefore, the area of the triangle is fraction numerator 1 over denominator 2 end fraction left parenthesis 5 minus square root of 2 end root right parenthesis left parenthesis square root of 10 end root right parenthesis asymptotically equal to 5.67. The correct answer is B.

Question Difficulty: 
medium