BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.6, Problem 91E
To determine

Find the original length of the reed.

Expert Solution

Answer to Problem 91E

  x=1±612cubits

Explanation of Solution

Calculation:

Here, let us suppose:

  x=Length of reedw=Width of fieldl=Length of fieldA=Area of field

Now, we have:

  1ninda=12cubits

We will convert it to square cubits, the area of field becomes:

  A=375ninda2A=375ninda21.144cubits21ninda2A=54000cubits2

We have to convert the word problem into equations and then solve it.

Now, we will translate the first measurement into an equation for the length of the field yields:

  l=60(x1)

Now, the second portion of the problem gives us equation for the width of the field in terms of the measurement of the reed:

  w=60x

Now, we are given the total area of the field so recalling the formula for area of a rectangle:

  A=w.l

Here, A is the area, w is the width, and l is the length.

  A=(60(x1))(60x)

Here, we are given the value for the area of the field, and we have already converted it to proper units, thus we get:

  54000=(60(x1))(60x)54000=(60x60)(60x)54000=3600x23600x3600x23600x54000=0

Now, we will solve it by using quadratic formula:

  x=(3600)±(3600)24(3600)(54000)2(3600)x=3600±12960000+7776000007200x=3600±7905600007200x=3600±3600617200x=1±612

Hence, the required answer is x=1±612cubits .

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