Factoring and problem solving - Help needed?
I really, really need help with these. I understand the nature of them but simply can't get them to work. Even showing me how to set them up(I got close with two of them) would be a huge help, and I'm confident in factoring outside these darned word problems...
1. The combined area of a square and a rectangle is 64 square cm. The width of the rectangle is 2cm more than the length of a side of the square, and the length of the rectangle is 2cm more than its width. Find the dimensions of the square and the rectangle.
2. The sum of the areas of two squares is 89 square cm. The length of a side of the larger square is 3cm more than the length of the side of the smaller square. Find the dimensions of each square.
3. The neighbors have an orchard that contains 90 trees. The number of trees in each row is 3 more than twice the number of rows. Find the number of rows and the number of trees per row.
Big thanks to whoever can help me out a little.
- 1 decade agoFavorite Answer
First of all, don't forget how to find the area of a square/rectangle. Here's a refresher: http://www.mathopenref.com/rectanglearea.html
Also, I use the * symbol to mean multiplication.
1. Okay, so we'll call the length and width of the rectangle L and W, respectively, and the side of the square (because they're all the same) S. The problem states W is 2 more than S, so S = W + 2. The combined area (S*S + L*W) is 64, so S*S + L*W = 64, and L is 2 more than W, so L = W + 2. Now you have three variables and three equations, so you should be able to solve that as a system of three equations. If you need to review that, check out this link: http://www.regentsprep.org/rEGENTS/MATH/syslin/Alg...
2. Same idea. We'll call the side of the larger square M and the side of the smaller one N. Combined area is 89, so M*M + N*N = 89, and larger side is 3 more than smaller side, so M = N + 3. This should be even easier than the last one, as you only have two variables to solve in your system.
[if you've got it this far, stop reading and try to do the last one on your own.]
3. Let T be trees in each row and R be the number of rows. Therefore, T*R will be the total number of trees, given as 90. T*R = 90. Also, T is 3 more than twice the number of rows (2R), so T = 2R + 3. Again, two variables, two equations.
Email me if you need further help or want to check your answers.Source(s): I'm kind of awesome at math.