Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms.

Option A

is the the ratio of corresponding sides for the similar triangles

Solution:

We have to write the ratio of corresponding sides for the similar triangles

When two figures are similar, the ratios of the lengths of their corresponding sides are equal.

The given figure in question is attached below with sides marked as ABC for bigger triangle and XYZ for smaller triangle

Therefore,

In the attached figure,

XY = 12

AC = 36

YZ = 13

CB = 39

Substituting these we get,

Reducing to lowest terms we get,

[ 36 divided by 12 is 3 and 39 divided by 13 is 3 ]

Thus Option A is correct

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)