Question

A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two congruent right triangles with areas of 44 square inches. Which statements are true? Check all that apply.

The area of the rectangle is 88 square inches.
The equation x(x – 3) = 44 can be used to solve for the dimensions of the triangle.
The equation x2 – 3x – 88 = 0 can be used to solve for the length of the rectangle.
The triangle has a base of 11 inches and a height of 8 inches.
The rectangle has a width of 4 inches.

Answer 1

True:
- The area of the rectangle is 88 square inches. (Each triangle is 44, so rectangle = 2·44 = 88.)
- The equation x^2 − 3x − 88 = 0 can be used to solve for the length (from x(x−3)=88).
- The triangle has a base of 11 inches and a height of 8 inches (solve x^2−3x−88=0 → x=11, width = 11−3 = 8).

False:
- x(x−3)=44 is incorrect (the triangle area gives (1/2)x(x−3)=44 → x(x−3)=88).
- The rectangle does not have width 4 inches (width = 8 inches).