the areas of three faces of a rectangular block are in the ratio 2:3:4 and its volume is 9000cm.fin the length of the shlrtest side
Answers
let the length of the shortest side be x
thus, area of each side:
2x, 3x, 4x
volume = 9m
according to question
2x + 3x +4x = 9000
9x = 9000
x = 9000/9
x = 1000
therefore area of shortest side =
2x
2×1000
2000cm^2 or 2m^2
Let the length of the rectangular block be l cm
Let the breadth of rectangular block be b cm
Let the height of the rectangular block be h cm
Ratio of three faces = 2:3:4
Area of smallest face (1st face) of the rectangular block => lb = 2x ----eq(1)
Area of 2nd face of rectangular block => bh = 3x ------eq(2)
Area of 3rd face => hl = 4x ----- eq(2)
Multiply eq(1), eq(2) and eq(3)
lh * bh * hl = 2x * 3x * 4x
(lbh)² = 24x³
(Volume of the rectangular block) ² = 24x³
(9000)² = 24x³
81000000 = 24x³
x³ = 81000000/24
x³ = 3375000
x = ∛ 3375000
x = 150
Substitute x = 3 in eq(1) and eq(2) to find the values
lb = 2(150)
lb = 300
l = 300/b --- eq (5)
bh = 3(150)
bh = 450
h = 450/b ---- eq(5)
Volume of the rectangular block = 9000 cc
lbh = 9000 cc
300/b * b * 450/b = 9000
300 * 450/b = 9000
450/b = 9000/300
450/b = 30
By cross multiplication
b = 450/30
b = 15 cm
substitute b = 15 in eq (4) and (5) to find the values of dimensions
l = 300/15
l = 20 cm
h = 450/15
h = 30 cm
Dimensions of the rectangular blocks are i.e, Length = 20 cm, Breadth = 15 cm and Height = 30cm
Among these dimensions 15 is the smallest one.
So, length shortest side is 15 cm