Quadrilateral Math has been dissected into squares. The area of the red square is 64 square units and the area of the blue square is 81 square units. Determine the dimensions and the area of Quadrilateral Math?
No idea what your diagram looks like.
To determine the dimensions and area of Quadrilateral Math, first, let's label the sides of the quadrilateral. Let's call the side length of the red square "x" and the side length of the blue square "y."
We know that the area of the red square is 64 square units, so we can write the equation: x^2 = 64.
To find the value of x, we need to take the square root of both sides of the equation: √(x^2) = √64. This simplifies to x = 8.
Similarly, the area of the blue square is 81 square units, so we can write the equation: y^2 = 81.
Taking the square root of both sides of the equation, we get y = 9.
Now we have the side lengths of the red square (x = 8) and the blue square (y = 9). To find the dimensions of Quadrilateral Math, we need to consider how these squares are dissected.
From the given information, we can deduce that the red square covers the upper left part of Quadrilateral Math, and the remaining part must be a rectangle with a side length equal to the difference between the side lengths of the red and blue squares (y - x).
So, the width of the rectangle is 9 - 8 = 1 unit.
To find the length of the rectangle, we note that along its length, it is made up of the side of the red square (8 units) and the side of the blue square (9 units). Thus, its length is the sum of the side lengths of the red and blue squares: 8 + 9 = 17 units.
Therefore, the dimensions of Quadrilateral Math are 17 units by 1 unit, and the area of Quadrilateral Math is calculated by multiplying its length and width: 17 * 1 = 17 square units.