Question

The areas of the three adjacent faces of a cuboidal box are 120 cm^2, 72 cm^2 and 60 cm^2 respectively. Find the length, breadth and height of the box.

Answer 1

Answer:

Length = 10 cm

Breadth = 12 cm

Height = 6 cm

Note :- As the faces and dimensions are not given respectively, the above values can be interchanged.

Step-by-step explanation:

Let the length be l, breadth be b, height be h.

Area of one face = l × b

Area of other face = b × h

Area of remaining face = l × h

$lb = 120 \: \: \: ...(1) \\ bh = 72 \: \: \: ...(2) \\ lh = 60 \: \: \: ...(3)$

From (1)

$l = \frac{120}{b} \: \: \: ...(4)$

Putting (4) in (3),

$\frac{120}{b} \times h = 60 \\ \frac{h}{b} = \frac{60}{120} = \frac{1}{2} \\ b = 2h \: \: \: ...(5)$

Putting (5) in (2),

$2h \times h = 72 \\ {h}^{2} = 36 \\ h = 6 \: cm$

Putting value of h in (5),

$b = 2h = 2 \times 6 = 12 \: cm$

Putting value of b in (1),

$l \times 12 = 120 \\ l = 10 \: cm$