Answer:
The playable area has a width of 9 inches and a height of 6 inches.
Step-by-step explanation:
There are a number of ways you can get there.
1. Check the answers to see which have the right area and aspect ratio.
A: area = 24 in² — does not match 54 in²
B: area = 54 in², aspect ratio 6:9 = 2:3 — does not match 3:2 aspect ratio
C: area = 54 in², aspect ratio 9:6 = 3:2 — matches problem statement
D: area = 121.5 in² — does not match 54 in²
2. If the screen were 3:2 (inches), its area would be 6 in². The area of 54 in² is 9 times that value, so the actual screen dimensions are √9 = 3 times 3:2. That is, they are width:height = 9:6 inches — matches selection C.
3. You can write equations for width and height and solve.
w/h = 3/2
wh = 54
Substituting w=3/2·h into the second equation gives
... (3/2)h·h = 54
... h² = 36 . . . . . multiply by 2/3
... h = √36 = 6 . . . . square root, result in inches
Answer:
D. The playable area has a width of 9 inches and a height of 6 inches.
Step-by-step explanation:
if the playable area is 54 and that such ratio of dimensions is 3:2
Then we are basically being asked to find the factor of ratios below that also multiply to get 54
54 = 9 x 6 and this is also a ratio of 3:2
As 3(3 + 2) = 54
and as width was asked first when ratio was given 3:2
The width therefore is 9 and the height is 6
So answer is D
