the area of a play ground is 96 sq yards. Find the dimensions.

Question

The diagram shows the length as (x+5) and the width as (x+15

Answer 1

(x+5) * (x+15) = 96

 

This is a quadratic equation, so there are 2 possible answers when we solve this.

 

x^2 +20x + 75 = 96

x^2 +20x -21 =0

 

Solving, we find the following two answers.

 

 

(x+21) * (x-1) =0

 

Set each equal to 0, and we get:

x+21 = 0 and x -1 = 0

which is the same as:

 

x= -21   and x = 1

Obviously, there is no negative distance, so the -21 with either the x+15 or the x + 5 would still be negative, and thus this answer is not possible.

 

So x = 1 should be possible. 

Let's prove if x = 1 is correct:

 

Proof:

 

(x+5) * (x+15) = 96

(1+5) * (1+15) = 96

6* 16 = 96

 

96 = 96, so to answer the question:

 

X+5 and x + 15, we find the dimensions of the Playground are 6yards, by  16 yards.

 

 

Answer 2

if the playground is rectangle shape, length = x+5, and width = x + 15, then we have

 

(x+5)(x+15) = 96 --> x²+20x + 75 = 96 --> x²+20x - 21 = 0 --> (x+21)(x-1) = 0 -->

 

either

x+ 21 = 0 --> x = -21 --> length = x+ 5 = -21 + 5 = -16 which is negative so this one is not acceptable

 

or x - 1 = 0 --> x = 1 --> length = x + 5 = 1 + 5 = 6 and width = x + 15 = 1 + 15 = 16 cool.

 

so the dimensions will be 6 and 16, we cam check by calculating the area again:

 

6 * 16 = 96