The distance between two points is X. The number of inches in X is equ

Question

The distance between two points is X. The number of inches in X is equal to the square root of the number of feet in X (1 foot =12 inches.) What is the length of X, in inches?

A. 144
B. 12
C. 1
D. 1/12
E. 1/144

chetan2u · Accepted Answer

Let the number of inches be a, so number of feet is  \frac{a}{12}

It is given that  \sqrt{\frac{a}{12}}=a

\frac{a}{12}=a^2

12a^2-a=0

a(12a-1)=0

So either  a=0  or  a=\frac{1}{12}

D

Bunuel · Answer

Say # of inches in X is  a , then # of feet in X is  \frac{a}{12} , (since 1 foot =12 inches).
Question: the length of X, in inches =  a  = ?

We are told that  a  is equal to the square root of  \frac{a}{12}  -->  a=\sqrt{\frac{a}{12}}  -->  a^2=\frac{a}{12}  -->  a=\frac{1}{12} .

Answer: D.

sumitkrocks · Answer

Let a be the number on inches in x

x= \sqrt{(a/12)}

Squaring

a^2=a/12
a=12a^2
1-12a^2=0
a=0 or a=1/12

Option D is the right answer

Fdambro294 · Answer

1st)

I would step back and look logically at the problem.

There are 12 inches in 1 foot.

Any length measured in inches will have a larger positive number than that same length measured in feet.

So how can:

(Measurement in inches) = sqrt(same measurement in FEET)

Because we are referring to the same length ——-The positive value we end up with for inches must be larger than the positive value we have for feet ——- for each foot (12 > 1)

(2)concept

When have a positive proper fraction that is between 0 and 1 ———> it will behave in the opposite manner with respect to exponents/roots as will positive numbers greater than 1

If 0 < X < 1

Then

(X)^2 < X < sqrt(X)

Taking the square root of the proper fraction will INCREASE the value of that positive proper fraction.

Therefore, in order to get a positive value in inches that will be larger than that same measurement in feet, the measurement in feet MUST be a positive proper fraction between 0 and 1

Eliminate A B and C. Leaves us with D and E

The next thing you can notice is that when you square D you will end up with E.

Again, since the same length measured in inches will have a larger pos. number than that same length measured in feet, picking D makes the most sense to test out.

1/12 inches ———>

converted to feet: (1/12) in * (1 ft) / (12 in)

———> 1/144 feet

1/12 inches is the equivalent measurement of 1/144 feet——- something with a length of 1/12 inches is 1/144 feet

The square root of (1/144) = (1/12)

The answer must be D because the question asks for the measurement in inches.

D

Posted from my mobile device

Regor60 · Answer

When a problem leaves something undefined one frequently has the flexibility to define it in a way that's convenient, as long as the rest of the problem doesn't place a constraint.

There being no such constraint, let's define the units of X as inches.

So the number of feet in X is 
X/12.

So the problem is stating:

X = (X/12)^.5

Squaring both sides and rearranging

X^2 - (X/12) = 0 or
X(X-(1/12)) = 0 or

X= 0 or X=1/12

If you didn't recognize that shortcut, then the rigorous way follows.

The distance is X in undefined units.

Let's call the unit "unit".

We're trying to find inches, so we need a conversion from units to inches.

Let's say there are Y inches/unit.

So the number of inches in X is:

X units * Y inches/unit =

XY inches

Since we know there is 1 foot/12 inches, we can calculate the number of feet by dividing XY by 12 =

XY/12 feet

We're told that:

XY = (XY/12)^.5

Squaring both sides =
(XY)^2 - XY/12 = 0

Or

XY(XY-1/12) = 0

So XY=0 or XY = 1/12 inches

Posted from my mobile device

Kinshook · Answer

Given: The distance between two points is X. The number of inches in X is equal to the square root of the number of feet in X (1 foot =12 inches.)

Asked: What is the length of X, in inches?

Let X = x inches = x/12 feet
 x = \sqrt{x/12} 
x^2 = x/12
x^2 - x/12 = 0
12x^2 - x = 0
x(12x-1) = 0
x = 0 or x=1/12
x = 1/12 inches since x=0 is not possible

IMO D

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The distance between two points is X. The number of inches in X is equ

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