Maths-
General
Easy

Question

The area of a base of a cuboid is 48 cm2 and its height and length of the diagonal are 3 cm and 13 cm respectively. Calculate the length and width of the box?

  1. 6 cm, 12 cm 
  2. 2 cm , 4 cm
  3. 12 cm , 4 cm
  4. 4 cm, 6 cm

Hint:

  The formula for the diagonal of a cuboid is = square root of open parentheses l squared plus b squared plus h squared close parentheses end root

The correct answer is: 12 cm , 4 cm


    Let a be the length and b be the width and c be height of rectangular solid whose area of the base will be (ab) m2 and

    length of diagonal = square root of a squared plus b squared plus c squared end root

    So accordingly

    (a)(b)=48 ……………..(1) and

    square root of a squared plus b squared plus c squared end root equals 13. text  or.  end text a squared plus b squared plus c squared equals 169

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a squared plus b squared equals 169 minus c squared end cell row cell a squared plus b squared equals 169 minus 9 end cell end table

    a2+b2=160-------------(2).

    Now using formula. (a + b)= a2+b2+2.ab

    (a + b)= 160 + 2 × 48

    (a + b)= 160 + 96 = 256

    Taking square root of both sides

    or. a + b = 16……………(3)

    and. (a - b)= a+ b- 2.ab

    ( a- b)= 160 – 96 = 64

    Taking square root of both sides

    or. a - b = 8…………………(4). ,

    By adding eqn. (3) and (4) we get,

    2a = 24.

    a = 24/2 = 12 m.

    Putting a = 12 in eqn. (3)

    12 + b = 16

    b = 16 – 12

    b = 4 m.

    Thus , length =12 m , width = 4 m.

    Therefore, the correct option is c)12cm , 4cm.

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