Question

A rectangular garden is 5m longer

Answer 1

Answer:

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

Step-by-step 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:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

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

$\displaystyle x=\frac{-5\pm \sqrt{5^2-4(1)(-600)}}{2(1)}$

Operating:

$\displaystyle x=\frac{-5\pm \sqrt{25+2400}}{2}$

$\displaystyle x=\frac{-5\pm \sqrt{2425}}{2}$

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