Question

Practice!

1.
In the diagram, JKLM~ EFGH.
C.
a.
b.
Find the scale factor of JKLM to EFGH.
k=
Find the values of x, y, and z.
x =
y =
Find the perimeter of each polygon.
4y + 4
H3G
11
zo
E 8 F
Z=
30
65°
M
20
D
K
L

Answer 1

a. To find the scale factor of JKLM to EFGH, we can compare the corresponding sides:

JK/JH = KL/KG = LM/LF = x/x = 1

Therefore, the scale factor is 1.

b. Since JKLM~EFGH, the corresponding sides are proportional. We can set up the following ratios:

JK/EF = KL/FG = LM/FH = 1/1

JK/x = KL/20

LM/30 = 1/2

Solving for JK, KL, and LM:

JK = EF = x

KL = 20(1/2) = 10

LM = 30(1/2) = 15

c. To find the perimeter of JKLM, we add the lengths of its sides:

Perimeter of JKLM = JK + KL + LM + MJ

Perimeter of JKLM = x + 10 + 15 + x

Perimeter of JKLM = 2x + 25

To find the perimeter of EFGH, we can use the fact that corresponding sides are proportional:

FG = KL = 10

FH = LM = 15

EG = JK = x

EH = EF = x√2

Perimeter of EFGH = EF + FG + GH + EH

Perimeter of EFGH = x + 10 + 2z + x√2

We are not given a value for z, so we cannot calculate the perimeter of EFGH.

Note: The angle measures given in the diagram are not used in the calculations for this problem.