Charlene is a video game designer and wants to make sure that her games can be played on all types of screens. in order for the games to work on both devices with a standard aspect ratio and those with widescreen aspect ratios, the playable area of the games should have an aspect ratio of 3: 2. this means that the width is equal to times the height. on one type of tablet, the playable area of the game on the screen is 54 square inches. write and solve a system of equations to determine the dimensions of the playable area. a. the playable area has a width of 6 inches and a height of 4 inches. b. the playable area has a width of 6 inches and a height of 9 inches. c. the playable area has a width of 9 inches and a height of 6 inches. d. the playable area has a width of 13.5 inches and a height of 9 inches.

C. The playable area has a width of 9 inches and a height of 6 inches.

There are a number of ways you can get there.

1. Check the answers to see which have the right area and aspect ratio.

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.

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 . . . . matches selection C

d? maybe

step-by-step explanation:

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this