Question

Mortimer wants to change the shape of his garden. The garden is now 3 feet longer than its wide, but if he increases the length by 4 feet and decreases the width by 1 feet, he will gain 8ft^2 in area. what are the original dimensions of the garden?

Answer 1

The original dimensions of the garden are

Length
`8\ ft`

Width
`5\ ft`

Explanation:

Let

x-----> the original length of the garden

y-----> the original width of the garden

we know that

`x=y+3` -----> equation A

The original area is equal to

`A=xy`

substitute equation A

`A=(y+3)y\\A=y^(2)+3y`

if he increases the length by 4 feet and decreases the width by 1 feet, he will gain 8ft^2 in area

so

The new area is equal to

`An=(x+4)(y-1)`

substitute equation A

`An=(y+3+4)(y-1)\\An=y^(2)-y+7y-7\\An=y^(2)+6y-7`

Remember that

`An=A+8`

substitute the values

`y^(2)+6y-7=y^(2)+3y+8`

`6y-3y=8+7`

`3y=15`

`y=5\ ft`

find the value of x

`x=5+3=8\ ft`

therefore

The original dimensions of the garden are

Length
`8\ ft`

Width
`5\ ft`