Bailey's rectangular dog pen for his irish setter must have an area of 400 square feet.

Question

Bailey's rectangular dog pen for his Irish setter must have an area of 400 square feet. Also, the length must be 10 feet longer than the width. Find the dimension of the pen.

 

Answer 1

L = 10 + W

 

L X W = 400

 

by substitution, in terms of W:  (10 + W) X W = 400

 

W^2 + 10W = 400

 

W^2 + 10W - 400 = 0; let's use x instead of w for the rest of it...

 

Simplifying
x2 + 10x + -400 = 0, however, there are no whole numbers which will satisfy, so:

Reorder the terms:
-400 + 10x + x2 = 0

Solving
-400 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + 10x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + 10x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + 10x + x2 = 0 + 400
10x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
10x + x2 = 400

The x term is 10x. Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 400 + 25

Reorder the terms:
25 + 10x + x2 = 400 + 25

Combine like terms: 400 + 25 = 425
25 + 10x + x2 = 425

Factor a perfect square on the left side:
(x + 5)(x + 5) = 425

Calculate the square root of the right side: 20.615528128

Break this problem into two subproblems by setting
(x + 5) equal to 20.615528128 and -20.615528128.

Subproblem 1
x + 5 = 20.615528128

Simplifying
x + 5 = 20.615528128

Reorder the terms:
5 + x = 20.615528128

Solving
5 + x = 20.615528128

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = 20.615528128 + -5

Combine like terms: 5 + -5 = 0
0 + x = 20.615528128 + -5
x = 20.615528128 + -5

Combine like terms: 20.615528128 + -5 = 15.615528128
x = 15.615528128

Simplifying
x = 15.615528128

 

so W = 15.6155 and L = 25.6155 and when you multiply the two, you obtain approx. 400 square feet...

 

 

 

Answer 2

w represents the width

w + 10 represents the length

 

400 = w(w + 10)

400 = w² + 10w

 

Can you solve for w?