Roger is creating designs with pieces of wood. Once piece is a equilateral triangle with a perimeter of 24 inches.

Question

Another pieces is a rectangle with one side the same length as a side of triangle.  The other side of the triangle is 3vinches shorter than a side of the triangle. Roger places the pieces together so that one side of the triangle touches a side of the rectangle that has the same length.

1. What are the dimensions of the triangle?

2. What are the dimensions of the rectangle?

3. Draw a sketch of the composite figure.

Find the perimeter of the composite figure.

Answer 1

If the triangle is equilateral (all sides equal length), and it's perimeter is 24 inches, then each side is 24/3 or 8 inches.

The dimensions of the triangle are equal 8" sides.

 

One side of the rectangle is the same length as one side of the triangle, so it is 8". It's opposite side will also be 8" because we know that rectangles have 2 sets of equal sides.

The other side of the rectangle is 3" shorter than a side of the triangle, so it is 5" (8-3=5). It's opposite side will also be 5".

 

I can't draw the sketch here, but it will have an 8x8x8" triangle butted up against an 8x5" rectangle, with the 8" side adjacent to the triangle. To find the perimeter, add the lengths of all exterior sides. Ignore the one side of the triangle and one side of the rectangle that are touching.

 

The perimeter of the composite figure should be the two remaining sides of the triangle, plus the three remaining sides of the rectangle.

 

Does that help?