Tia used a photocopier to dilate the design for a monorail track system. The figure shows the design and its photocopy: Two irregular quadrilaterals ABCD and EFGH are drawn. EFGH is the photocopy of design ABCD. AB measures 17 meters, BC measures 14 meters. No dimensions on EFGH are shown. The ratio of DA:HE is 1:2. What is the length, in meters, of side FG on the photocopied image?

FG = 28 meters

Step-by-step Explanation:

==>A design ABCD and its dilated photocopy EFGH.

Length of side AB = 17m

BC = 14m

DA:HE = 1:2

==>Required:

Length of side FG on the photocopy EFGH, in meters.

==>Solution:

Dilation of design ABCD would, upon transformation would produce a photocopy EFGH that is similar. Thus, ABCD ~ EFGH

Since ABCD is similar to EFGH, it means the ratio of their corresponding sides would be the same, and also have the same scale factor.

Therefore, it means DA:HE = BC:FG

Therefore, let's find length of side FG of the photocopy using the ratio1:2 that is given for DA:HE, which would also apply as the scale factor or ratio for all other corresponding sides.

Thus,

1:2 = BC:FG

1:2 = 14:FG

1/2 = 14/FG

Cross multiply to solve for FG

1×FG = 14×2

FG = 28 meters

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5