ABCD is a rectangle with AB=26, BC=11. X, Y and Z are points on AB, BC and CD, respectively, such that AX=BY=CZ=6. What is the area of triangle XYZ?
To find the area of triangle XYZ, we can first find the lengths of XY and YZ using the given information.
Let's start by considering triangle AXY. We know that AX = 6, and AB = 26. Since XY is a side of the triangle, we can subtract AX from AB to find the length of XY:
XY = AB - AX = 26 - 6 = 20.
Now let's consider triangle CYZ. We know that CZ = 6, and BC = 11. Since YZ is a side of the triangle, we can subtract CZ from BC to find the length of YZ:
YZ = BC - CZ = 11 - 6 = 5.
Now that we know the lengths of XY and YZ, we can use them to find the area of triangle XYZ. The formula for the area of a triangle is:
Area = (base * height) / 2.
In this case, XY is the base and YZ is the height. Therefore, we have:
Area = (XY * YZ) / 2 = (20 * 5) / 2 = 100 / 2 = 50.
So, the area of triangle XYZ is 50 square units.