Question

A rancher has a square cow pen with side length x. He decides to change the shape

of the pen while still using the same amount of fencing materials. The equation

(x + 10)(x - 10) = 300 represents the relationship of the new side lengths (in feet)

of the pen and its area (in square feet).

a. If 300 represents the area of the new cow pen, what do the expressions

(x + 10) and (x - 10) each represent?

b. Find x, the original side length (in feet) of the square pen. Show your reasoning.

Answer 1

Answer:

a) x+ 10 is the length of the ranch

x - 10 is the width of the ranch

b) 20 feet

Step-by-step explanation:

Area of the square ranch = L²

L is the side length of the ranch

If the equation

(x + 10)(x - 10) = 300 represents the relationship of the new side lengths (in feet)

Then we can find x where;

x + 10 is the new length of the ranch

x - 10 is the new width of the ranch

Open the parenthesis

equation

(x + 10)(x - 10) = 300

x²²-10x + 10x - 100 = 300

x² - 100 = 300

x² = 300+100

x² = 400

x = √400

x = 20

Hence the original length of the square pen is 20 feet

Answer 2

The values (x + 10) and (x - 10) represents the length and width of the new pen.

The value of x, the original length of the pen is 20 cm

How to find the side of a square?

The pen is a square. It was later reconstructed to form the following expression.

(x + 10)(x - 10) = 300

where

• area = 300  feet squared

Therefore,

(x + 10)(x - 10) = 300

x² - 10x + 10x - 100 = 300

x² - 100 = 300

x² = 300 + 100

x² = 400

x = √400

x = 20 ft

Therefore, the original side length of the square pen is 20 ft.

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