SOLUTION: a rectangle garden is ten m longer than it is wide. the owner wants to increase the size of the garden. if he adds an additional 3m to each of the four sides, he will gain an addit

Question 181580: a rectangle garden is ten m longer than it is wide. the owner wants to increase the size of the garden. if he adds an additional 3m to each of the four sides, he will gain an additional 216 m squared of the garden area. what are the dimensions of the garden?
i just dont get these. my teacher has tried to explainthem to me multiple times. i just cant seem to get past writing the first part : x+10 and x and then the bigger one's x+13 and x. help?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You have the original dimensions correct, namely x and x + 10. But Mr. Gardener wants to add 3 meters to each side of the garden. That means 3 meters on the top, 3 on the bottom, 3 on the left, and 3 on the right.

That means that the new dimensions are x + 3 + 3 = x + 6 and x + 10 + 3 + 3 = x + 16.

The added area is 216 square meters, which would be the area of the new, larger garden, given by

minus the area of the original garden, given by

. Think of it as a rectangular sheet of paper which has an area that is the length times the width, then you cut a rectangular hole in the center of it, subtracting an area that is the length times the width of the hole, leaving you with a picture frame looking thing.

So, putting it all together, you can say:

The area of the new garden minus the area of the old garden is 216 square meters. Symbolically stated:

.

So multiply using FOIL and the distributive property and collect all like terms, leaving the 216 on the right. The result will be a simple single variable linear equation that can be solved for the value of x.

John

RELATED QUESTIONS
Sam Stratton is planning a garden 25 m longer than it is wide. The garden will have an... (answered by richwmiller)

Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase (answered by jim_thompson5910)

A farmer wants to make a vegetable garden such that length is 3 meters longer than the... (answered by Theo)

A rectangular garden has 88 feet of fencing around it. The garden is 4 feet longer than... (answered by ewatrrr)

Donna has a garden that is 30 ft by 36 ft. She wants to increase the size of the garden... (answered by Marz157,MathTherapy)

the length of a patio garden is 11ft longer than it is wide. if the garden is 20ft long,... (answered by Alan3354)

A rectangular garden is three times longer as it is wide. If the area of the garden is... (answered by Stitch)

Alex\ is\ building\ a\ rectangular\ garden\ that\ has\ an\ area\ of\ 912\ square\ feet.\... (answered by josgarithmetic,Alan3354)

dan o leary has decided to plant a garden. he wants to make to make it 10.1 m long and... (answered by checkley77)