SOLUTION: The perimeter of a rectangle is 24 feet. a. If x is the measure of one side of the rectangle, represent the measure of an adjacent side in terms of x. b. If y is the area of th

Algebra ->  Trigonometry-basics -> SOLUTION: The perimeter of a rectangle is 24 feet. a. If x is the measure of one side of the rectangle, represent the measure of an adjacent side in terms of x. b. If y is the area of th      Log On


   

Question 697406: The perimeter of a rectangle is 24 feet.
a. If x is the measure of one side of the rectangle, represent the measure of an adjacent side in terms of x.
b. If y is the area of the rectangle, express the area in terms of x.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
The formula for perimeter is:
+P+=+2x+%2B+2z+
I'm calling one side +x+ and the adjacent side z
given:
+P+=+24+
+24+=+2x+%2B+2z+
Subtract +2x+ from both sides
+24+-+2x+=+2z+
Divide both sides by +2+
+12+-+x+=+z+
The adjacent side is +12+-+x+ ft
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(b)
given:
Area = +y+
The formula for area, using my variables, would be
+A+=+x%2Az+
+y+=+x%2Az+
and, since
+z+=+12+-+x+
+y+=+x%2A%28+12+-+x+%29+
+y+=+12x+-+x%5E2+