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The base of a rectangular box has dimensions of 15 by 6 cm^2. What is

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Bunuel
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The base of a rectangular box has dimensions of 15 by 6 cm^2. What is [#permalink] New post   24 Apr 2023, 01:30
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The base of a rectangular box has dimensions of 15 by 6 cm^2. What is the height of the box, if the sum of the areas of the base and top is equal to the sum of the areas of the four sides ?

A. 15/7 cm
B. 4 cm
C. 30/7 cm
D. 5 cm
E. 40/7 cm



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ChandlerBong
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The base of a rectangular box has dimensions of 15 by 6 cm^2. What is [#permalink] New post   24 Apr 2023, 06:22
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Area of base + Area of Top = 15 * 6 * 2 = 180 cm\(^2\) --- (1)

Assume the height as "h".

Sum of the area of 4 sides = (6 * h)*2 + (15 * h)*2 = 42h --- (2)

Now we equate (1) and (2) -> 42h = 180 cm\(^2\) --> we get h = 30/7 cm.
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Re: The base of a rectangular box has dimensions of 15 by 6 cm^2. What is [#permalink] New post   24 Apr 2023, 10:19
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Bunuel wrote:
The base of a rectangular box has dimensions of 15 by 6 cm^2. What is the height of the box, if the sum of the areas of the base and top is equal to the sum of the areas of the four sides ?

A. 15/7 cm
B. 4 cm
C. 30/7 cm
D. 5 cm
E. 40/7 cm



My instinct is to set up an algebraic equation or two AND the answer choices are just numbers. When both of those things are true, the odds are very good that I can get to the right answer at least as quickly and with very little risk of a silly mistake using Plugging In The Answers (PITA). I like trying B and D.

B:
Base + top = 2(15*6) = 2(90) = 180
Four sides = 2(15*4)+2(6*4) = 2(60)+2(24) = 120+48 = 168
Base + top > four sides

D:
Base + top = 2(15*6) = 2(90) = 180
Four sides = 2(15*5)+2(6*5) = 2(75)+2(30) = 150+60 = 210
Base + top < four sides

We need something in between. Only once answer choice is in between.

Answer choice C.


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tejas99
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Re: The base of a rectangular box has dimensions of 15 by 6 cm^2. What is [#permalink] New post   24 Apr 2023, 23:47
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We have to form a equation for solving this question.
base area is given and top area will be same to base.
so it will become 2*90 = 180

now sides will have area which can be calculated based on the l*h or b*h
so we will get equation like 180= 2(15*h) + 2(6*h)

solve this and you will get answer.

Answer is 30/7
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Re: The base of a rectangular box has dimensions of 15 by 6 cm^2. What is [#permalink] New post   26 Apr 2023, 23:46
Area of base + Area of Top = 15 * 6 * 2 = 180 cm 2

Now questions says,
Sum of area of base and top = sum of areas of 4 sides
180 = 2(LH) + 2(BH)
180 = 2(LH +BH)
90 = H (L+B)
H = 90/ 21 (Since L+H = 15+6 = 21)
Therefore, dividing by 3, we get H = 30/7
Option C
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Re: The base of a rectangular box has dimensions of 15 by 6 cm^2. What is [#permalink]
26 Apr 2023, 23:46
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