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A wall paper , 312m long …

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A wall paper , 312m long and 25 cm wide is required to cover the walls of a room. Length of the room is 7m and its breadth is twice its height . Determine the hight of the room.

    • Posted by Thunder ?Yashwanth??? 6 years, 4 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 4 months ago

    Length of wallpaper =312 m,

    Breadth of wallpaper=25 cm =0.25 m

    Area of wallpaper = 312 {tex}\times{/tex} 0.25 = 78.00 m2
    Length of room = 7 m
    Let height be x m, then it's  breadth is 2x m
    Surface area of four walls = 2 [lh + bh]
    = 2 (7x + 2x2)
    = 14x + 4x2
    According to the question

    Surface area of four walls= Area of wallpaper
    4x2 + 14x = 78 {tex}\Rightarrow{/tex} 2x2 + 7x - 39 = 0
    {tex}\Rightarrow{/tex} 2x2 + 13x - 6x - 39 = 0
    {tex}\Rightarrow{/tex} x(2x + 13) - 3 (2x + 13) = 0
    {tex}\Rightarrow{/tex}(x - 3) (2x + 13) = 0
    {tex}\Rightarrow{/tex} x - 3 = 0 or 2x + 13 = 0
    {tex}\Rightarrow{/tex} x = 3 or x = -{tex}\frac{13}{2}{/tex}(rejected) {tex}\Rightarrow{/tex} x = 3 m
    Hence, height of the room is 3 m.

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