Another question that I came across in GMAT Prep
Question : What is the area of the triangle PQR given P(4,0) Q(0,3) R(7,4)?
A. 12.5
B. 14
C. 10√2
D. 16
E. 25
Answer: [spoiler]A[/spoiler]
Though this sounds simple, I aint able to solve it...
What is the area of triangle??
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You could:
1)Draw a sketch of PQR on x-y axes.
2)Now draw a rectangle to surround it, vertices: (0,0), (0,4), (7,0), (7,4)
3) Work out the area of the rectangle R = 7 * 4 = 28
4) Work out the areas of the 3 triangles inside the rectangle that surround triangle PQR:
Triangle 1: Area = 1 * 7/2 = 3.5
Triangle 2: Area = 4 * 3/2 = 6
Triangle 3: Area = 3 * 4/2 = 6
Sum of 3 triangle areas, S = 15.5
5) Subtract R - S = 28 - 15.5 = 12.5
Answer (A) 12.5
Does this help?
1)Draw a sketch of PQR on x-y axes.
2)Now draw a rectangle to surround it, vertices: (0,0), (0,4), (7,0), (7,4)
3) Work out the area of the rectangle R = 7 * 4 = 28
4) Work out the areas of the 3 triangles inside the rectangle that surround triangle PQR:
Triangle 1: Area = 1 * 7/2 = 3.5
Triangle 2: Area = 4 * 3/2 = 6
Triangle 3: Area = 3 * 4/2 = 6
Sum of 3 triangle areas, S = 15.5
5) Subtract R - S = 28 - 15.5 = 12.5
Answer (A) 12.5
Does this help?
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Thanks mathsbuddy!!
Now I get it!!
Now I get it!!
Mathsbuddy wrote:You could:
1)Draw a sketch of PQR on x-y axes.
2)Now draw a rectangle to surround it, vertices: (0,0), (0,4), (7,0), (7,4)
3) Work out the area of the rectangle R = 7 * 4 = 28
4) Work out the areas of the 3 triangles inside the rectangle that surround triangle PQR:
Triangle 1: Area = 1 * 7/2 = 3.5
Triangle 2: Area = 4 * 3/2 = 6
Triangle 3: Area = 3 * 4/2 = 6
Sum of 3 triangle areas, S = 15.5
5) Subtract R - S = 28 - 15.5 = 12.5
Answer (A) 12.5
Does this help?
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Here's a similar question to practice with:
- https://www.beatthegmat.com/geometry-que ... 70467.html
Cheers,
Brent
- https://www.beatthegmat.com/geometry-que ... 70467.html
Cheers,
Brent
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Question : What is the area of the triangle PQR given P(4,0) Q(0,3) R(7,4)?
A. 12.5
B. 14
C. 10√2
D. 16
E. 25
The area of the rectangle drawn around triangle PQR = 7*4 = 28.
Since triangle PQR takes up less than half the rectangle, PQR < 14.
The correct answer is A.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Hi sbhawal,
The other responses to this post each provide explanation and insight into this question. Here are some tactics to keep in mind as you come across these issues in future questions:
1) Many graphing questions can be made easier to solve by graphing them.
2) Any diagonal line on a graph is part of a right triangle. You can draw that triangle to figure out the length of the line and the area of the triangle.
GMAT assassins aren't born, they're made,
Rich
The other responses to this post each provide explanation and insight into this question. Here are some tactics to keep in mind as you come across these issues in future questions:
1) Many graphing questions can be made easier to solve by graphing them.
2) Any diagonal line on a graph is part of a right triangle. You can draw that triangle to figure out the length of the line and the area of the triangle.
GMAT assassins aren't born, they're made,
Rich