uptetd16p1 q93
- Option : C
- Explanation : (C) Area of three adjacent faces of a cuboid are in the ratio of 7: 10 : 14.
Let area of three faces be 7x, 10x, and 14x.
Let the length, breadth and height of cuboid be l, b and h, respectively.
Volume of cuboid = 350 cm3
⇒ l × b × h = 350 cm3 ........(i)
According to the figure,
l × b = 14x .........(ii)
l × h = 7x ..........(iii)
b × h = 10x ............(iv)
On multiplying (ii), (iii) and (iv)
l2b2h2 = (14x)(7x)(10x)
⇒ (lbh)2 = (14 × 7 × 10)x3
⇒ (350)2 = (980)x3
x3 = 125 ⇒ x = 5
Area of the faces are
7x = 7 × 5 = 35 = l × h
10x = 10 × 5 = 50 = b × h
14x = 14 × 5 = 70 = l × b
Put the value of l × h = 35 in Eq (i), then
l × b × h = 350
⇒ 35 × b = 350
⇒ b = 10 cm
Similarly,
l × b × h = 350
⇒ l × 50 = 350
⇒ l = 7 cm
and l × b × h = 350
⇒ 70 × h = 350
⇒ h = 5 cm
∴ Longest side has a length of 10 cm.
