Aaron bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow him to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on? (SHOW WORK)

Accepted Solution

Answer:The scale factor is equal to 1/2The dimensions of each channel when splits the screen is 46 in x 38 inStep-by-step explanation:we know thatThe dimensions of the new television is 92 in x 76 inRemember thatIf two figures are similar, then the ratio of its areas is equal to the scale factor squaredLetA1 -----> the area of the new televisionA2 ----> the area of each channel when splits the screenz-----> the scale factor[tex]z^{2} =\frac{A2}{A1}[/tex]we have thatThe area of the new television is 4 times the area of each channel[tex]A1=4A2[/tex][tex](A2/A1)=1/4[/tex][tex]z^{2} =\frac{1}{4}[/tex][tex]z=\frac{1}{2}[/tex] -----> the scale factorsoWhen splits the screen, the dimension of each channel is equal to92/2 in x 76/2 inso46 in x 38 inRemember, if two figures are similar then the scale factor is equal to the ratio of their corresponding sidesVerify the value of the scale factor92/46=1/2or76/38=1/2