Answer:
A. The area of the rectangle is 88 square inches.
C. The equation x² – 3x – 88 = 0 can be used to solve for the length of the rectangle.
Step-by-step explanation:
The question is incomplete. Here is the complete 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.
A.The area of the rectangle is 88 square inches.
B.The equation x(x – 3) = 44 can be used to solve for the dimensions of the triangle.
C.The equation x2 – 3x – 88 = 0 can be used to solve for the length of the rectangle.
D.The triangle has a base of 11 inches and a height of 8 inches.
The rectangle has a width of 4 inches.
If a rectangular piece of paper has a width that is 3 inches less than it's length and it is cut in half along a diagonal to create two congruent right triangles with areas of 44 square inches, the width of the rectangle will be equal to the base of the each of the triangle, and the length equal to the height of the triangle.
Let the length of the rectangular piece of paper be L. If its width is 3 inches less than it's length, then W = L-3
The base of the triangle = L-3 and the height = L
Area of the triangle = 1/2 * base * height
Area of the triangle = 1/2 (L-3)L
If the area of the congruent triangles is 44in², then;
44 = 1/2 (L-3)L
88 = (L-3)L
88 = L²-3L
L²-3L-88=0
L²-11L+8L-88=0
L(L-11)+8(L-11)=0
(L-11)(L+8)= 0
L = 11in
This shows that the height of the triangle is 11 inches.
The base of the triangle = 11-3 = 8 inches
The area of the rectangle = Length*Breadth
= 11* 8
= 88in²
Based on the calculation above, the following statements are true.
-The area of the rectangle is 88 square inches.
-The equation x² – 3x – 88 = 0 can be used to solve for the length of the rectangle.
