The fence surrounding a rectangular garden is 168 feet long. The length of the garden is 14 feet longer than i?
The fence surrounding a rectangular garden is 168 feet long. The length of the garden is 14 feet longer than its width. How many square feet are in the garden?
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Tags: rectangular, feet, longer, Fence, Garden, long.Related posts:
Area = 14 * i
Perimeter = 2(14 + i) + 2(i)
so simplify perimeter –> 28 + 2i + 2i
perimeter = 28 + 4i = 168
i = 35 feet
so the garden is 35 feet by (14 + 35) feet
Area = 35 * 49…
let the width of the rectangular garden = w feet
then the length of the rectangular garden = w + 14 feet
perimeter of the rectangular garden is 2( w + w +14 ) = 4w + 28 feet
so
4 w + 28 = 168 feet
=> 4w = 140
=> w = 35 feet
then length of the garden = 35 + 14 = 49 feet
area of the garden = length * width = 49 * 35 = 1715 sq feet
Okay first thing is to identify your variables;
A=area= your answer and what you want
W= width
L = length
P=Perimeter
Okay now that you have that its just turning the sentences into equations. 9 out of 10 times the question will tell you everything you need to know and nothing extra so assume that if you haven’t used all the numbers that your missing something. So what do you initially know before the problem?
P=2L+2W which is a rectangle
A=WL
Now plug in the numbers from the question: P=168 and L=W+14
so:
168=2L+2W and L = W+14
84=L+W (simplifying)
84=(W+14) +W (substituting)
84=2W +14 (simplifying)
70=2W (simplifying)
W=35 (simplifying)
Plugging W back into L= W+14 and L =49 (substitution)
A=WL
A= 35*49
A= 1715 ft^2