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Find the dimension of a rectangle A rectangle is 10ft longer than it's width. The width...
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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
X^2 + 10X = 1824
adding 25 on both sides of equation we get
X^2 + 10x + 25 = 1849
(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.
Posted by krishna-agrawala on July 22, 2009 at 9:51 AM (Answer #2)
Middle School Teacher
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?
Posted by cburr on July 22, 2009 at 1:26 PM (Answer #3)
High School Teacher
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.
Posted by neela on July 25, 2009 at 3:49 AM (Answer #4)
dimension is length x breadth
Posted by sowbagia on December 10, 2011 at 4:14 PM (Answer #5)
base times height or bxh
Posted by rockonhunter on December 15, 2011 at 7:34 AM (Answer #6)
The area of a rectangle is 45 square cm. If the length is 4 cm greater than the width, what is the dimensions of the rectangle?
The picture below shows the rectangle with the area of 45cm2. Now, let the width be w. Since, the length is 4cm greater than the width, the length will be w+4 cm.
Before we can find the dimensions of the rectangle, we need find w first. Here's how:
1) Write an equation that relates 45cm2, w+4 and w.
To do so, we know that the area of the rectangle, 45cm2 can be found by multiplying w with w+4. Hence, we have:
To continue, we need to remove the bracket and simplify the equation. This is shown below:
Posted by ngyunhui on December 23, 2011 at 12:31 PM (Answer #7)
dimension is length x breadth
work it out from that :)
Posted by angelems789 on December 29, 2011 at 1:11 AM (Answer #8)
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