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09 Jun 2020, 06:44
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A
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Difficulty:
35%
(medium)
Question Stats:
68% (02:24) correct
32%
(02:20)
wrong
based on 28
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What is the longest distance between two points in a rectangular solid if the area of its faces is 50, 75 and 150 square units respectively?
A. 5√14
B. 3√70
C. 10√7
D. 14√5
E. Cannot be determined
A. 5√14
B. 3√70
C. 10√7
D. 14√5
E. Cannot be determined
Updated on: 12 Jun 2020, 06:54
Originally posted by GMATinsight on 09 Jun 2020, 07:05.
Last edited by GMATinsight on 12 Jun 2020, 06:54, edited 1 time in total.
Last edited by GMATinsight on 12 Jun 2020, 06:54, edited 1 time in total.
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Bunuel
CONCEPT:
Longest distance in a Cuboid \(= \sqrt{l^2+b^2+h^2}\)
Longest distance in a Cuboid \(= \sqrt{l^2+b^2+h^2}\)
50 = (25*2) or (5*10)
75 = (25*3) or (5*15)
150 = (25*6) or (15*10)
i.e. Sides are {5, 10, 15}
i.e. Longest distance here \(= \sqrt{5^2+10^2+15^2} = \sqrt{(25+100+225)} = √350 = 5√14\)
Answer: Option A
General Discussion
Siak0730
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09 Jun 2020, 07:14
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Let a, b, c be sides of rectangular solid
Area of faces are given
Let
a*b=50 ...... 1
b*c=75 ...... 2
c*a=150 ......3
Substituting value of a(=50/b) and c(=75/b) from 1 and 2 respectively in 3 we get
(50*75)/(b*b)=150
Or b*b=25
Or b=5
Substituting value of b in 1 and 2 we get
a=10,c=15
Now the longest distance between 2 sides in a normal rectangle is it's diagonal ends
Diagonal length basically
let a and b be sides so
(a^2+b^2)^1/2 = diagonal length
But we are given solid rectangle
It means cuboid
Longest distance in cuboid is the space diagonal defined as (a^2+b^2+c^2)^1/2
Putting values of a, b, c
We get
5((14)^1/2) or A
Posted from my mobile device
Area of faces are given
Let
a*b=50 ...... 1
b*c=75 ...... 2
c*a=150 ......3
Substituting value of a(=50/b) and c(=75/b) from 1 and 2 respectively in 3 we get
(50*75)/(b*b)=150
Or b*b=25
Or b=5
Substituting value of b in 1 and 2 we get
a=10,c=15
Now the longest distance between 2 sides in a normal rectangle is it's diagonal ends
Diagonal length basically
let a and b be sides so
(a^2+b^2)^1/2 = diagonal length
But we are given solid rectangle
It means cuboid
Longest distance in cuboid is the space diagonal defined as (a^2+b^2+c^2)^1/2
Putting values of a, b, c
We get
5((14)^1/2) or A
Posted from my mobile device
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