the area of a rectangular door is 21 ft2. the border around the door is 20ft. what is the length and width of the door?

Question

the area of a rectangular door is 21 ft2. the border around the door is 20ft. what is the length and width of the door?

 

I cant understand why the border is smaler than the area

Answer 1

Area = L x W = 21 ft²

Border (perimeter) = 2L + 2W = 20 ft.

solving for W in the first equation gives W = 21/L

and substituting into the second equation gives

2L + 2(21/L) = 20

Multiplying all terms by L gives

2L² + 42 = 20L or L² - 10L + 21 = 0

Factoring to solve for L gives (L -7) (L -3) = 0

and L = 7 or L = 3.

Let L = 7, then W = 3.

Area and perimeter are measures of different quantities so it is OK for the area to be numerically larger than perimeter!

Answer 2

It seems the border is another term for perimeter rather than the border is outside the door

 

Answer 3

Suppose the door is a 3 by 7 rectangle. The area is 7*3=21 square feet.

The border is in linear feet, not square feet.

The door is a rectangle whose perimeter is 7+3+7+3=20 feet

The border is around the door but there are only three sides to the border-two lengths and one width because there is no border at the bottom of the door.

The border has to be 20 feet so you could have a border that is 8 feet on each side and 4 feet at the top.

8+8+4=20