Question

A rectangular garden is 5m longer

than it is wide.
The area of the garden is 600m2
Calculate the width and length of the garden.​

Answer 1

The width of the garden is 22.12 m and its length is 27.12 m

Explanation:

Equations

Let x = width of the garden

The length is 5 m longer than the wide, thus:

x + 5 = length of the garden

The area of the rectangular garden is

A=x(x+5)=600

Operating:

`x^2+5x-600=0`

Solving with the quadratic formula:

`\displaystyle x=(-b\pm √(b^2-4ac))/(2a)`

Where a=1 b=5 c=-600:

`\displaystyle x=(-5\pm √(5^2-4(1)(-600)))/(2(1))`

Operating:

`\displaystyle x=(-5\pm √(25+2400))/(2)`

`\displaystyle x=(-5\pm √(2425))/(2)`

There are two solutions:

x = 22.12

x = -27.12

The negative solution is not valid because x is the width of the garden, thus

x = 22.12 m

And

y = 22.12 + 5 = 27.12 m

The width of the garden is 22.12 m and its length is 27.12 m