I would like to know are there articles regarding these two questions?
In the rectangular coordinate plane system, the area of the triangle PQR is what fraction of the area of the triangle LMN?The following coordinates are given P(6,0) Q(8,4), R(10,0) L(2,0) M(8,12), and N(14,2)
a) 1/9 b) 1/8 c) 1/6 d) 1/5 e) 1/3
An arc is give with 100ft as the legs of the arc. The question states that the figure is a quarter of a circle. Then it goes on to say: If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?
a) 278 b) 341 c) 357 d) 400 e) 441
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Maciek
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Hi CrmnKnwls!
IMO B
Formula for the area of the triangle is
A = 0.5 * base * height = 0.5 * b * h
or
A = |( Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By))/2|
Ax and Ay are the x and y coordinates of the point A, Bx and By are the x and y coordinates of the point B, and
Cx and Cy are the x and y coordinates of the point C.
A(PQR)/A(LMN) = ?
b = |PR| = 4
h = 4
A(PQR) = 0.5 * 4 * 4 = 8
Triangle LMN:
it is more difficult to calculate height so let us use the second formula
A(LMN) = |( Lx(My - Ny) + Mx(Ny - Ly) + Nx(Ly - My))/2|
A(LMN) = |( 2(12 - 2) + 8(2 - 0) + 14(0 - 12))/2)| = |( 20 + 16 - 14*12)/2| = |(36 - 168)/2| = 66
A(PQR)/A(LMN) = 8/66 = 4/33
the closest answer is b
hope it helps!
Best,
Maciek
IMO B
Formula for the area of the triangle is
A = 0.5 * base * height = 0.5 * b * h
or
A = |( Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By))/2|
Ax and Ay are the x and y coordinates of the point A, Bx and By are the x and y coordinates of the point B, and
Cx and Cy are the x and y coordinates of the point C.
A(PQR)/A(LMN) = ?
Triangle PQR:The following coordinates are given P(6,0) Q(8,4), R(10,0) L(2,0) M(8,12), and N(14,2)
b = |PR| = 4
h = 4
A(PQR) = 0.5 * 4 * 4 = 8
Triangle LMN:
it is more difficult to calculate height so let us use the second formula
A(LMN) = |( Lx(My - Ny) + Mx(Ny - Ly) + Nx(Ly - My))/2|
A(LMN) = |( 2(12 - 2) + 8(2 - 0) + 14(0 - 12))/2)| = |( 20 + 16 - 14*12)/2| = |(36 - 168)/2| = 66
A(PQR)/A(LMN) = 8/66 = 4/33
the closest answer is b
hope it helps!
Best,
Maciek
An arc is give with 100ft as the legs of the arc. The question states that the figure is a quarter of a circle. Then it goes on to say: If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?
a) 278 b) 341 c) 357 d) 400 e) 441
"There is no greater wealth in a nation than that of being made up of learned citizens." Pope John Paul II
if you have any questions, send me a private message!
should you find this post useful, please click on "thanks" button
if you have any questions, send me a private message!
should you find this post useful, please click on "thanks" button
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diebeatsthegmat
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Maciek wrote:Hi CrmnKnwls!
IMO B
Formula for the area of the triangle is
A = 0.5 * base * height = 0.5 * b * h
or
A = |( Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By))/2|
Ax and Ay are the x and y coordinates of the point A, Bx and By are the x and y coordinates of the point B, and
Cx and Cy are the x and y coordinates of the point C.
A(PQR)/A(LMN) = ?
Triangle PQR:The following coordinates are given P(6,0) Q(8,4), R(10,0) L(2,0) M(8,12), and N(14,2)
b = |PR| = 4
h = 4
A(PQR) = 0.5 * 4 * 4 = 8
Triangle LMN:
it is more difficult to calculate height so let us use the second formula
A(LMN) = |( Lx(My - Ny) + Mx(Ny - Ly) + Nx(Ly - My))/2|
A(LMN) = |( 2(12 - 2) + 8(2 - 0) + 14(0 - 12))/2)| = |( 20 + 16 - 14*12)/2| = |(36 - 168)/2| = 66
A(PQR)/A(LMN) = 8/66 = 4/33
the closest answer is b
hope it helps!
Best,
Maciek
how come h= 4 here?An arc is give with 100ft as the legs of the arc. The question states that the figure is a quarter of a circle. Then it goes on to say: If the land is enclosed by a fence, which of the following is closest to the length, in feet, of the fence?
a) 278 b) 341 c) 357 d) 400 e) 441
how come h= 4 here?
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Maciek
- Master | Next Rank: 500 Posts
- Posts: 164
- Joined: Sun Jul 18, 2010 5:26 am
- Thanked: 49 times
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- GMAT Score:710
hi!
h = 4 because points P and R are on X-axis so you can simplify calculation:
h = Qy - 0 = 4
You can still use second formula to calculate the area of triangle PQR
A = |( Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By))/2|
A = |( Px(Qy - Ry) + Qx(Ry - Py) + Rx(Py - Qy))/2|
A = |( 6(4 - 0) + 8(0 - 0) + 10(0 - 4))/2| =
= |( 24 + 0 + -40)/2| = |( -16)/2| = 8
hope it helps!
Best,
Maciek
h = 4 because points P and R are on X-axis so you can simplify calculation:
h = Qy - 0 = 4
You can still use second formula to calculate the area of triangle PQR
A = |( Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By))/2|
A = |( Px(Qy - Ry) + Qx(Ry - Py) + Rx(Py - Qy))/2|
A = |( 6(4 - 0) + 8(0 - 0) + 10(0 - 4))/2| =
= |( 24 + 0 + -40)/2| = |( -16)/2| = 8
hope it helps!
Best,
Maciek
"There is no greater wealth in a nation than that of being made up of learned citizens." Pope John Paul II
if you have any questions, send me a private message!
should you find this post useful, please click on "thanks" button
if you have any questions, send me a private message!
should you find this post useful, please click on "thanks" button
