### Algebraic Expressions Divisible by 3

Problem If a+2 is divisible by 3, which of the following expressions is/are also divisible by 3? A. 3+2a B. 5a-2 C. 8+7a D. 1+5a Solution When a number is divisible by 3 then it is a multiple of 3. So, if it is given that a+2 is divisible by 3 then a+2 is a…

### How to find the equation given the roots

Before I answer the question in the title, we need to do some revisions: This is what you do when you solve a quadratic equation like : Solution: => (x-5)(x+2)=0 => If x-5 = 0, then x = 5; if x+2 = 0, then x =-2. The solution is x=5 or x=-2. If you graph…

### Perpendicular Bisectors of Triangles

What is a perpendicular bisector? A perpendicular bisector of a line segment is a line that makes a 90-degree angle (a right angle) at the midpoint of a segment. In the figure, line b is the perpendicular bisector of line segment AB at C. This implies AC=CB and the measure of the angles at C…

### Which rectangle has a bigger area?

ABCD is a square and G is a point on its diagonal. Obviously, the two colored rectangles have equal area: ab.   What about in the figure below? Problem: ACDB is a rectangle. E is a point on the diagonal.  Which rectangle has a bigger area? GEIA or FEHD? Answer The diagonal divides a rectangle…