i need help with a word problem

Question

my word problem is the only one i have not been able to answer. It reads-

A square and a rectangle have the same area. One side of the rectangle is 3 feet shorter than the square while the other side is 4 feet longer than the square. Find the length of one side of the rectangle.

Answer 1

Terry has the side of the square correctly written out. If the problem is asking you about the sides of the rectangle as noted in the question I saw, then follow up Terry's calculation by figuring out each side of the rectangle using the original information:

First side of rectangle is X-3 so 12-3 gives you 9 and second side is X+4 which gives you 12+4 or 16. Either answer of 9 or 16 would be considered to be correct for the problem that asks "Find the length of one side of the rectangle". You can then check your work by calculating the area of the rectangle and comparing it to the area of the square: area of rectangle = 9X16=144 which is same as area of square 12X12=144 so we can be sure that the values 9 and 16 make sense.

Answer 2

Terry

We had a triangle sneak in here. I'm not sure if that was supposed to say "square", so I'll answer it as such.

Let X = side of square

Then the sides of the rectangle are (X-3) and (X+4) and the area is (X-3)(X+4). This in turn equals the area o f the square, X². Since the two are equal, we can set it to

X² = (X-3)(X+4) and distribute to get

X² = X² +4X - 3X - 12. Cleaning up, we get

X² = X² + X - 12. Subtracting X² from both sides and adding 12 to both sides, we get

12 = X

--------

There is not enough information in the problem to solve it including the triangle. Asking for one side of the triangle leads one to assume that the triangle is equilateral, but that could be a false assumption. There is also no additional relationship between the square and the triangle or the rectangle and the triangle to be able to solve this problem for three shapes.