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

Answer:

The original dimensions of the garden are

Length $8\ ft$

Width $5\ ft$

Step-by-step 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 $5\ ft$