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.
Answers
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
case A) The area of the rectangle is square inches
The statement is True
See the procedure
Case B) 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
case C) The equation can be used to solve for the length of the rectangle
The statement is True
see the procedure
case D)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
case E) The rectangle has a width of inches
The statement is False
See the procedure
The correct statements are:
- The area of the rectangle is 88 square inches.
- The equation x^2 – 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.
What are the dimensions of the rectangle?
When a rectangle is split diagonally, two right triangles are formed.
The area of a triangle = 1/2 x base x height
44 = 1/2 × (x - 3) × x
Where x represents the length
In order to determine the value of x, take the following steps:
Multiply both sides of the equation by 2: 88 = x² - 3x
x² - 3x - 88 = 0
Use the factorisation method to find x: (x² + 8x) (-11x - 88x)
x(x + 8) -11(x + 8)
x + 8 = 0
x = -8
x - 11 = 0
x = 11
Width = 11 - 3 = 8
Area of the rectangle = length x width
11 x 8 = 88 square inches.
To learn more about how to determine the area of a triangle, please check: brainly.com/question/9329354
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