You are planning to put a new digital flat TV on a wall that is 12 ft long and 9 ft high. The digital TV has a diagonal of 72 inches. The length of the TV is twice the width of the TV. How much of the wall will still need to be decorated around the TV?

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Answer 1 · 2018-07-23T01:50:07

#color(purple)("Area of wall to be decorated around T V " = 105.6 " sq ft"#

#"Area of the wall " A_W= 12 * 9 = 108 "sq ft"#

Now, we have to find the area of the TV.

"Area of TV = Length * Width" = l * w#

#"But we know, l = 2 * w#

#:. "T V Area " A_T = l * w = 2 w * w = 2 w^2#

#"Diagonal " d = 72 " inch "= 6 '#

By Pythagoras theorem, d^2 = l^2 + w^2 = (2w)^2 + w^2 = 5 w^2#

#d^2 = 5 w^2 = 6 " or " w^2 = 6/5 #

#A_T = 2 w^2 = 12 / 5 " sq ft"#

#"Diff. between area of wall and the TV " A_D = 108 - 12/ 5 = 105.6 "sq ft"#