RE: GMAT Practice Questions

[CrmnKnwls]

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

[Maciek]

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) = ?

The following coordinates are given P(6,0) Q(8,4), R(10,0) L(2,0) M(8,12), and N(14,2)

Triangle PQR:

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

[BastiG]

Can you pls post the source of these questions? I don't think that at least the first question won't be in the GMAT because it takes far too long!

[diebeatsthegmat]

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) = ?

The following coordinates are given P(6,0) Q(8,4), R(10,0) L(2,0) M(8,12), and N(14,2)

Triangle PQR:

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?

[Maciek]

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