SOLUTION: a garden in the form of a square is surrounded by a walkway 2m wide. What are the dimensions of the garden if the area of the walkway is 800 square metres?

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Question 614990: a garden in the form of a square is surrounded by a walkway 2m wide. What are the dimensions of the garden if the area of the walkway is 800 square metres?
Answer by nerdybill(7384) (Show Source):
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a garden in the form of a square is surrounded by a walkway 2m wide. What are the dimensions of the garden if the area of the walkway is 800 square metres?
.
Let x = length of one side of garden
then
(x+4)(x+4)= 800
x^2+8x+16= 800
x^2+8x-784= 0
applying the "quadratic formula" we get:
x = {24.28, -32.28}
throw out the negative solution (extraneous) leaving:
x = 24.28 m
.
details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=3200 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 24.2842712474619, -32.2842712474619. Here's your graph: