Choose an appropriate scale and construct a scale drawing of each rectangular state to fit on a 4-by-6-inch index card. The state of Colorado is approximately 380 miles long (east to west) and 280 miles wide (north to south). The state of Wyoming is approximately 365 miles long (east to west) and 265 miles wide (north to south).

1:8,632,800

Step-by-step explanation:

we have a 4-by-6-inch index card on which the state of Colorado and Wyoming should be drawn, so we must add the areas of the two states and adapt them in scale , for this we must add the width of the two states (within 4 inches) and the length (within 6 inches) of them  

According graph:

380 miles+365 miles=745 miles (long)

265 miles+280 miles=545 miles (wide)

if 545 miles ≡ 4 inch

    x miles    ≡ 1 inch

1 inch ≡ 136.25 miles, but 1 mile ≡ 63,360 inch, so

1 inch (index card) ≡ (63,360 inch * 136.25 miles) = 8,632,800 inch in the reality, then 545 miles = 34,531,200 inch and 745 miles= 47,203,200, inch

This to say that:

34,531,200 inch / 8,632,800 inch/mile = 4 inch

47,203,200 / 8,632,800 inch/mile = 5.46 inch

finally,

the scale is 1:8,632,800  ≡ 1 inch in the index card = 8,632,800 in the reality or 1 inch in the index card = (8,632,800/63360) 136.25 miles in the reality

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3