Atriangle drawn on a map has sides of lengths 7 cm, 10 cm, and 15 cm. the shortest of the corresponding real-life distances is 97 km. find the longest of the real-life distances. round to the nearest tenth as needed.

The Longest distance is 207.857 km round it we get 207.9 km

Step-by-step explanation:

The shortest distance on map is 7 cm which correspond with shortest distance of 97 km

The longest distance on map is 15 cm which correspond with shortest distance of "x" km

to find "x"

we have form this equation

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation: