SOLUTION: Please help me solve this problem: Valerie needs to to put a fence around her pool and deck. The area to be fenced is rectangular in shape such that the length is 2 feet longer tha

Algebra ->  Linear-equations -> SOLUTION: Please help me solve this problem: Valerie needs to to put a fence around her pool and deck. The area to be fenced is rectangular in shape such that the length is 2 feet longer tha      Log On


   

Question 1018243: Please help me solve this problem: Valerie needs to to put a fence around her pool and deck. The area to be fenced is rectangular in shape such that the length is 2 feet longer than the width. If she needs a total of 140 feet of fencing, what are the dimensions (length and width) of the area to be fenced?
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
w for width, L for length;
Perimeter is given 140, so equation for it is 2w%2B2L=140. Simplified, this becomes w%2BL=70.

Described and put symbolically also, L=w%2B2.

Solve the system, system%28w%2BL=70%2CL=w%2B2%29.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +L+ = length of pool and deck in feet
Let +W+ = width of pool and deck in feet
given:
(1) +L+=+W+%2B+2+
The formula for perimeter is:
(2) +P+=+2L+%2B+2W+
Substitute (1) into (2)
(2) +P+=+2%2A%28+W+%2B+2+%29+%2B+2W+
(2) +P+=+2W+%2B+4+%2B+2W+
(2) +P+=+4W+%2B+4+
You are given that +P+=+140+ ft
(2) +140+=+4W+%2B+4+
(2) +4W+=+136+
(2) +W+=+34+
and
(1) +L+=+W+%2B+2+
(1) +L+=34+%2B+2+
(1) +L+=+36+
The dimensions are: 34 x 36 ft2
----------------------------
check:
+140+=+2L+%2B+2W+
+140+=+2%2A36+%2B+2%2A34+
+140+=+72+%2B+68+
+140+=+140+
OK