1003 more square feet of wallpaper for the living room than the family room when family room is with dimensions (l = 3x, b = 3x, h = x), living room is with dimensions (l = 5x, b = 3x, h = x) and doors are with dimension (b =3, h = 7) {where x = 8}. This can be obtained by forming equations for the given figures.
<h3>What is the expression of square feet of wallpaper for family room?</h3>
Given that,
dimensions (l = 3x, b = 3x, h = x) and there is one door (b =3, h = 7)
expression of square feet of wallpaper for family room,
⇒ area of four walls - area of one door= [(3x)(x)+(3x)(x)+(3x)(x)+(3x)(x)] - [3×7]
=[3x²+3x²+3x²+3x²] - 21
=12x² - 21 square feet
<h3>What is the expression of square feet of wallpaper for living room?</h3>
Given that,
height and width are same as of the family room but length is 5 times more than height [length = 5(height) ⇒ l = 5x]
dimensions (l = 5x, b = 3x, h = x) and there is two doors (b =3, h = 7)
expression of square feet of wallpaper for family room,
area of four walls - area of two doors= [(3x)(x)+(5x)(x)+(3x)(x)+(5x)(x)] - 2[3×7]
=[3x²+5x²+3x²+5x²] - 2(21)
=16x² - 42 square feet
<h3>
What is the total amount of wallpaper needed?</h3>
total amount of wallpaper needed
⇒wallpaper for family room + wallpaper for living room = 12x²-21 + 16x²-42
=28x²-63 square feet
<h3>
How much more square feet the living room will require more than family room when x = 8?</h3>
- Family room ⇒ 12x²-21 = 12(8²)-21 = 768-21=747 square feet
- Living room ⇒ 16x²-42 = 16(8²)-42 = 1792-42 = 1750 square feet
Area of wallpaper of living room - area of wallpaper of family room
= 1750 - 747
= 1003 square feet
Hence 1003 more square feet of wallpaper for the living room than the family room when family room is with dimensions (l = 3x, b = 3x, h = x), living room is with dimensions (l = 5x, b = 3x, h = x) and doors are with dimension (b =3, h = 7) {where x = 8}.
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