Let
x-------> the length of the rectangle
y------> the width of the rectangle
we know that
The area of the rectangle is equal to
The area of the two congruent right triangles is equal to the area of the rectangle
so
-------> equation A
-----> equation B
Substitute equation B in equation A
--------> equation that can be used to solve for the length of the rectangle
Using a graph tool-------> solve the quadratic equation
see the attached figure
The solution is
-----> the length of the rectangle
Find the value of y
----> the width of the rectangle
Statements
<u>case A)</u> The area of the rectangle is square inches
The statement is True
See the procedure
<u>Case B)</u> The equation can be used to solve for the dimensions of the triangle
The statement is False
Because, the equation can be used to solve for the dimensions of the triangle
<u>case C)</u> The equation can be used to solve for the length of the rectangle
The statement is True
see the procedure
<u>case D)</u>The triangle has a base of inches and a height of
inches
The statement is True
Because, the base of the triangle is equal to the length of the rectangle and the height of the triangle is equal to the width of the rectangle
<u>case E)</u> The rectangle has a width of inches
The statement is False
See the procedure
