Question

1. jklm ~ efgh

a) find the scale factor.
b) find the values of x, y, and c.
c) find the perimeter of each trapezoid.

Explanation:

Step1: Identify corresponding sides

Corresponding sides: $JK=20$ and $EF=11$, $JM=30$ and $EH=y$, $KL=x$ and $FG=8$, $ML=c$ and $GH=3$

Step2: Calculate scale factor (JKLM to EFGH)

Scale factor $= \frac{JK}{EF} = \frac{20}{11}$
(Or EFGH to JKLM: $\frac{11}{20}$; we use JKLM as the larger figure)

Step3: Solve for $x$ (JKLM to EFGH inverse)

$x = 8 \times \frac{20}{11} = \frac{160}{11} \approx 14.55$

Step4: Solve for $y$

$y = 30 \times \frac{11}{20} = \frac{330}{20} = 16.5$

Step5: Solve for $c$

$c = 3 \times \frac{20}{11} = \frac{60}{11} \approx 5.45$

Step6: Find perimeter of EFGH

Perimeter $= 8 + 11 + 3 + 16.5 = 38.5$

Step7: Find perimeter of JKLM

Perimeter $= 20 + \frac{160}{11} + \frac{60}{11} + 30 = 50 + \frac{220}{11} = 50 + 20 = 70$

Answer:

a) Scale factor (JKLM to EFGH) is $\frac{20}{11}$; (EFGH to JKLM) is $\frac{11}{20}$
b) $x = \frac{160}{11}$, $y = 16.5$, $c = \frac{60}{11}$
c) Perimeter of EFGH is $38.5$; Perimeter of JKLM is $70$