Eveline made a scale drawing of a patio she is planning to build.
1 cm
2.5 m
A 12 cm
C: 13 cm
B: 5 cm
Which proportion could Eveline use to find the length of side A?
1 cm
2.5m
13 cm
xm
1 cm
12cm

StartFraction 1 centimeter over 2.5 meters EndFraction = StartFraction 12 centimeters over x meters EndFraction

Step-by-step explanation:

The complete question is

Eveline made a scale drawing of a patio she is planning to build.

1 centimeter = 2.5 meters. Triangle A B C. Side A is 12 centimeters, side B is 5 centimeters, and side C is 13 centimeters.

Which proportion could Eveline use to find the length of side A?

StartFraction 1 centimeter over 2.5 meters EndFraction = StartFraction 13 centimeters over x meters EndFraction

StartFraction 1 centimeter over 2.5 meters EndFraction = StartFraction 12 centimeters over x meters EndFraction

StartFraction 12 centimeters over 2.5 meters EndFraction = StartFraction x centimeters over 1 meter EndFraction

StartFraction 1 centimeter over 12 meters EndFraction = StartFraction 2.5 centimeters over x meters EndFraction

The picture of the question in the attached figure

we know that

The scale drawing is

That means

1 cm in the drawing represent 2.5 m in the actual

using proportion

Find out the actual length of side A if in the drawing the length is 12 cm

solve for x

The length of side A is 30 meters

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!