Peter's pool table is 1 ft longer than twice its width. The area of the pool table is 15 f t2. Find the dimensions of the pool table.

Answer 1

Hello, Reggion,

I'll use W for the width and L for the length, both in feet.

We are told that the length is twice the width, plus 1: L = 2W + 1

We know that L*W = Area, which is 15 ft² so: L*W = 15 ft²

Use the equation for length in the second equation:

L*W = 15 ft²

(2W + 1)*W = 15 ft²

2W² + W - 15 = 0

Factor:

(W + 3)*(2W - 5) = 0

Therefore, there are two possible answers:

W = -3, and

W = (5/2)

We can't have a negative length, unless we are in a Star Wars movie. The answer is the remaining solution: W = 2.5 ft

Length is found from the first equation: L = 2W + 1

L = 2(5/2) + 1

L = 6 ft

Multiply the two values for L and W to see if we get 15 ft².

(5/2 ft)*(6 ft) = 15 ft²

The answers work. L = 6 ft and W = 2.5 ft.

Bob

Answer 2

Since length is described in terms of width, start with width as w.

width is w

So length is 1 foot longer than twice the width w. Length is 2w+1.

Area = length times width.

15 = (2w+1)(w)

or

15=w(2w+1)

Simplify 15=w(2w+1) by distributing the w.

Then set the equation = to zero by subtracting 15 so you have a quadratic equation in standard form 0=ax²+bx+c.

Use a quadratic solving technique to solve for x. Factoring or the quadratic formula.