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

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 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) = ?

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