Maths-
General
Easy
Question
A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width x, in inches, of the box?
- 0 < x ≤ 10
- 0 < x ≤ 11
- 0 < x ≤ 17
- 0 < x ≤ 20
The correct answer is: 0 < x ≤ 10
HINT – Form a linear inequality by taking ‘x’ as width of the base of the box (as given) and ‘y’ as length of the base of the box
SOLUTION – Let length of the base of the box = y inches
Let width of the base of the box = x inches (given)
It is given that height of the box = 60 inches
Sum of perimeter of the base and height of the prism < 130 inches
2( x + y) + 60 ≤ 130 ---- (1)
Also, it is given that length = 2.5 
width
y = 2.5x ---- (2)
Putting value of (2) in (1) we get,
2( 2.5 x + x) + 60 ≤ 130
2( 3.5 x) ≤ 70
7 x ≤ 70
x ≤ 10
Since width is always positive so x > 0
So, we get 0 < x ≤ 10
Hence option A is correct
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