We are going to form a triangle of base 10 inches ans height 5 finches; also, the eight of our triangle will be the width of our rectangle (a rectangle is a parallelogram). First, we are going to use the area of a triangle formula: [tex]A= \frac{1}{2} bh[/tex]
where
[tex]A[/tex] is the area in square inches
[tex]b[/tex] is the base of the triangle
[tex]h[/tex] is the height of the triangle
We know that [tex]b=10[/tex] and [tex]h=5[/tex], so lets replace those values in our formula:
[tex]A= \frac{1}{2} (10)(50)[/tex]
[tex]A= \frac{1}{2}(50) [/tex]
[tex]A=25[/tex]
Now that we have the area of our triangle, we are going to use the area of a rectangle formula: [tex]A=wl[/tex]
where
[tex]A[/tex] is the area in square inches
[tex]w[/tex] is the width of the rectangle
[tex]l[/tex] is the length of the rectangle
Since the width of our rectangle is equal to the height of our triangle, [tex]w=5[/tex]. Also, we know for our problem that the area of our triangle and the area of our triangle must be equal, so [tex]A=25[/tex]. Lets replace those values in our formula to find the length of our rectangle:
[tex]A=wl[/tex]
[tex]25=5l[/tex]
[tex]l= \frac{25}{5} [/tex]
[tex]l=5[/tex]
We can conclude that the dimensions of our triangle are: base=10 inches and height= 5 inches, and the dimensions of our parallelogram are: width= 5 inches and length= 5 inches.
