Question

3. A rancher in Colorado needs to build a square pen for the cattle this winter. He figured he needs an arca
about 625 square yards. What are the dimensions of his pen?​

Answer 1

Answer:

Cattle Pen

A rancher wants to use a fence as an enclosure for a rectangular cattle pen with area 400 square feet.

a. Suppose he decides to make one side of the pen 40 feet long. Draw a picture and label the length of each side of the pen. What is the length of each side? What is the total amount of fence needed?

b. What would be the total amount of fence needed if the pen were a square?

c. Can two rectangles with the same area have different perimeters?

d. Find a formula for a function F = F(l) that gives total amount of fence, in feet, required in terms of the length l, in feet, of one of its sides. (Hint: First draw a picture of the pen and label one side l. Next figure out the lengths of the other sides in terms of l.)

Step-by-step solution:

Step 1 of 3

a)

Area of the rectangular cattle pen is 400 square feet

One side of the pen is 40 feet

Let is the length of other side

Hence length of each side is

Chapter 1.4, Problem 16E is solved.

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Corresponding Textbook

Functions and Change (4th) edition 9781111785024 1111785023

Functions and Change | 4th Edition

9781111785024ISBN-13: 1111785023ISBN: Bruce CrauderAuthors: Rent | Buy

Alternate ISBN: 9780547156699

Functions and Change

(4th Edition)

Solutions for Chapter 1.4 Problem 16E

Problem 16E: A Cattle Pen A rancher wants to use a fence as an enclosur...

Solutions for Problems in Chapter 1.4 is solved

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Answer 2

The dimension of the yard side is 25 yard

Given:

625 square yards of area for a square pen

To find :

Dimension of yard

Solution:

We know the area of any square = $(side of the square)^{2}$

here;

$625 = (a)^{2}$    [ let us assume the side of the square is = a yard ]  

$then , \sqrt{625} =a$

therefore; the side of the square pen is 25 yard

The dimension of the yard side is 25 yard

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