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A rectangle is 10ft longer than it's width. the width of the surrounding deck is 3inches on each side. If the area is 1824sq.ft, Find the dimension of the outside edge of the deck.

To solve this problem we must first find out the dimension of the rectangle.

To do this let us assume that

width of the rectangle is X ft.

Then the length will be = X + 10

Then area of the rectangle =  X * (X + 10) = 1824

Therefore

X^2 + 10X = 1824

adding 25 on both sides of equation we get

X^2 + 10x + 25 = 1849

Therefore

(X + 5)^2 = 1849

(X + 5) = 43

X = 43 - 5 = 38

Therefore the rectangle is 38 ft wide and 48 ft long.

As the deck is 3 inch (0.25 ft) wide the dimensions of the outer edge of deck are:

38.5 ft wide by 48.5 ft long.

It's not possible to answer this question accurately without resolving the ambiguity about area.  Is 1824 sq ft the area of the rectangle, or of the deck?

Going through the discussions I put forth my view to solve the  problem with the kind of situations that arose among we mathematics friends:

Assume that the area of the rectangle without the deck =1824. Then the length and breadth without deck is a solution of  product of breadth, x  and length,x+10 = 1824 : x(x+10)=x^2+10x=1824. Or x^2+10x-1824=0. or (x-38)(x+48)=0. So, x=38  feet is breadth and x=38+10=48 feet is the length of the rectangle.

The area of the deck = Area of outer rectangle -area of inner rectangle:

[38'+2*3'') ][48'+2*3"]-1824 sq ft = 38.5'*48.5'-1824 sq ft.=[1867.25 -1824] sq ft= 43.25 sq ft.

Therefore, the outer dimensions of the deck are: breadth 38.5' , length 48.5'  and inner dimensions:38 ft and 48 ft and area of the deck 43.75 sq ft.

If you assume that 1824 sq ft is the area of the rectangle inclusive of the 3" border, then the area of the deck around the rectangle = [1824-(38-0.5)(48-0.5) ] sq ft=[1824-37.5*47.5] sq ft= [1824-1781.25] sq ft. = 42.75 sq ft.

Deck dimension : 38' by 48' outer . 37.5' by 47.5' inner and the deck area =42.75 sq ft.

If you assume the deck area =1824 sq ft, then also the deck  area = outer area-inner area of the rectangles:

(x+0.5)(x+10.5)-x(x+10)=1824. giving x=1824-5.25. So, the length and breadth of deck  (both outer measurements) = 1818.25 feet and 1828.25 feet.

If the deck is consired within edge of rectangle, then x(x+10)-(x-0.5)(x+9.5) = 1824 . So, x=1824-4.75=1819.25feet.And x+10=1829.25 feet.