Alina has 15x + 12 yards of ribbon. She uses 6x - 3 yards for a project. How many yards does she have left?
1 answer:
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Given:
The matrix is .
To find:
The determinant of given matrix, i.e, .
Solution:
If a matrix is A of order , then the value of the determinant of that matrix is equal to the element of that matrix.
For example: Let A be the matrix of order .
Then,
The given matrix is . So, the determinant of given matrix, i.e,
, is
Therefore, the value of determinant of given matrix is -8.
Note that no diagram is drawn to scale.
If the diagram in the first picture is further worked upon, we have polygon ABCDE.
Note also that line AD = 18in and line MD = 10in.
This simply means the line Am = AD - MD = 8in.
We have the height of the triangle needed to solve for the area of the triangle. Area of Triangle = 1/2×b×h
Where b is length base of the triangle and h is the length of height of the triangle.
We still need b to find the Area.
Note also that two opposite sides of parallelograms are equal. This implies that line DC = line EB which is equal to 14in.
In the third image, you can see this. Half the length of the side of the parallelogram is needed. This means 14/2 = 7in.
We can now solve for the Area of the triangle.
We have the are of the triangle to be 28in. Multiply this by 3 to find the total area of all three triangles since the three triangles are identical. Thus,
Total Area of all Triangles = 28×3 = 76in
Now, find the area of the two parallelograms.
Area of parallelogram EBCD = bh
Where b is the length of the base side and h is the height.
Hence from the diagram,
Area of parallelogram EBCD is 140in.
Total Area of both Parallelograms will be 140 ×2= 280in since both are identical.
To find the Total Area of the tile pattern add the area of the triangles and the Parallelograms. This is 76 + 280 =356in.
Your answer is 356in.
If the diagram in the first picture is further worked upon, we have polygon ABCDE.
Note also that line AD = 18in and line MD = 10in.
This simply means the line Am = AD - MD = 8in.
We have the height of the triangle needed to solve for the area of the triangle. Area of Triangle = 1/2×b×h
Where b is length base of the triangle and h is the length of height of the triangle.
We still need b to find the Area.
Note also that two opposite sides of parallelograms are equal. This implies that line DC = line EB which is equal to 14in.
In the third image, you can see this. Half the length of the side of the parallelogram is needed. This means 14/2 = 7in.
We can now solve for the Area of the triangle.
We have the are of the triangle to be 28in. Multiply this by 3 to find the total area of all three triangles since the three triangles are identical. Thus,
Total Area of all Triangles = 28×3 = 76in
Now, find the area of the two parallelograms.
Area of parallelogram EBCD = bh
Where b is the length of the base side and h is the height.
Hence from the diagram,
Area of parallelogram EBCD is 140in.
Total Area of both Parallelograms will be 140 ×2= 280in since both are identical.
To find the Total Area of the tile pattern add the area of the triangles and the Parallelograms. This is 76 + 280 =356in.
Your answer is 356in.