Question

A rectangular garden is 20ft longer then it is wide. it’s area is 525ft squared. What are it’s dimensions?

Answer 1

L=35 and w=15 see attached picture for steps

Answer 2

The dimensions of the rectangular garden: Width = 15 feet and Length = 35 feet.

Solution:

Let the width of the rectangular garden be ‘b’ ft . Then the length of the rectangular garden is ‘b+20’ width.

In the question it is given that the area of the rectangular garden is 525 ft.

We know,

`Area of rectangle = length* width`

`\Rightarrow525 = (b+20)* b`

`\Rightarrow525 = b^2+20b`

`\Rightarrow b^2+20b - 525 = 0`

`\Rightarrow b^2+35b - 15b -525 =  0`

On taking the common terms out we get,

`\Rightarrow b(b+35)-15(b+35) = 0`

`\Rightarrow(b-15)(b+35) = 0`

Therefore, Either
`(b-15) = 0` or
`(b+35) = 0`

`b=+15` or
`b=-35`

Taking the positive value of b i.e. b= 15 we get width of the rectangular field to be 15 feet and the length of the rectangular garden to be
`(b + 20) = 15+20 = 35 feet.`